two version of R2R are hereHEADmaster

16 files changed, 3672 insertions, 0 deletions

diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/__init__.py b/.venv/lib/python3.12/site-packages/networkx/linalg/__init__.py
new file mode 100644
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+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/__init__.py
@@ -0,0 +1,13 @@
+from networkx.linalg.attrmatrix import *
+from networkx.linalg import attrmatrix
+from networkx.linalg.spectrum import *
+from networkx.linalg import spectrum
+from networkx.linalg.graphmatrix import *
+from networkx.linalg import graphmatrix
+from networkx.linalg.laplacianmatrix import *
+from networkx.linalg import laplacianmatrix
+from networkx.linalg.algebraicconnectivity import *
+from networkx.linalg.modularitymatrix import *
+from networkx.linalg import modularitymatrix
+from networkx.linalg.bethehessianmatrix import *
+from networkx.linalg import bethehessianmatrix
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/algebraicconnectivity.py b/.venv/lib/python3.12/site-packages/networkx/linalg/algebraicconnectivity.py
new file mode 100644
index 00000000..c94972a5
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/algebraicconnectivity.py
@@ -0,0 +1,657 @@
+"""
+Algebraic connectivity and Fiedler vectors of undirected graphs.
+"""
+
+from functools import partial
+
+import networkx as nx
+from networkx.utils import (
+    not_implemented_for,
+    np_random_state,
+    reverse_cuthill_mckee_ordering,
+)
+
+__all__ = [
+    "algebraic_connectivity",
+    "fiedler_vector",
+    "spectral_ordering",
+    "spectral_bisection",
+]
+
+
+class _PCGSolver:
+    """Preconditioned conjugate gradient method.
+
+    To solve Ax = b:
+        M = A.diagonal() # or some other preconditioner
+        solver = _PCGSolver(lambda x: A * x, lambda x: M * x)
+        x = solver.solve(b)
+
+    The inputs A and M are functions which compute
+    matrix multiplication on the argument.
+    A - multiply by the matrix A in Ax=b
+    M - multiply by M, the preconditioner surrogate for A
+
+    Warning: There is no limit on number of iterations.
+    """
+
+    def __init__(self, A, M):
+        self._A = A
+        self._M = M
+
+    def solve(self, B, tol):
+        import numpy as np
+
+        # Densifying step - can this be kept sparse?
+        B = np.asarray(B)
+        X = np.ndarray(B.shape, order="F")
+        for j in range(B.shape[1]):
+            X[:, j] = self._solve(B[:, j], tol)
+        return X
+
+    def _solve(self, b, tol):
+        import numpy as np
+        import scipy as sp
+
+        A = self._A
+        M = self._M
+        tol *= sp.linalg.blas.dasum(b)
+        # Initialize.
+        x = np.zeros(b.shape)
+        r = b.copy()
+        z = M(r)
+        rz = sp.linalg.blas.ddot(r, z)
+        p = z.copy()
+        # Iterate.
+        while True:
+            Ap = A(p)
+            alpha = rz / sp.linalg.blas.ddot(p, Ap)
+            x = sp.linalg.blas.daxpy(p, x, a=alpha)
+            r = sp.linalg.blas.daxpy(Ap, r, a=-alpha)
+            if sp.linalg.blas.dasum(r) < tol:
+                return x
+            z = M(r)
+            beta = sp.linalg.blas.ddot(r, z)
+            beta, rz = beta / rz, beta
+            p = sp.linalg.blas.daxpy(p, z, a=beta)
+
+
+class _LUSolver:
+    """LU factorization.
+
+    To solve Ax = b:
+        solver = _LUSolver(A)
+        x = solver.solve(b)
+
+    optional argument `tol` on solve method is ignored but included
+    to match _PCGsolver API.
+    """
+
+    def __init__(self, A):
+        import scipy as sp
+
+        self._LU = sp.sparse.linalg.splu(
+            A,
+            permc_spec="MMD_AT_PLUS_A",
+            diag_pivot_thresh=0.0,
+            options={"Equil": True, "SymmetricMode": True},
+        )
+
+    def solve(self, B, tol=None):
+        import numpy as np
+
+        B = np.asarray(B)
+        X = np.ndarray(B.shape, order="F")
+        for j in range(B.shape[1]):
+            X[:, j] = self._LU.solve(B[:, j])
+        return X
+
+
+def _preprocess_graph(G, weight):
+    """Compute edge weights and eliminate zero-weight edges."""
+    if G.is_directed():
+        H = nx.MultiGraph()
+        H.add_nodes_from(G)
+        H.add_weighted_edges_from(
+            ((u, v, e.get(weight, 1.0)) for u, v, e in G.edges(data=True) if u != v),
+            weight=weight,
+        )
+        G = H
+    if not G.is_multigraph():
+        edges = (
+            (u, v, abs(e.get(weight, 1.0))) for u, v, e in G.edges(data=True) if u != v
+        )
+    else:
+        edges = (
+            (u, v, sum(abs(e.get(weight, 1.0)) for e in G[u][v].values()))
+            for u, v in G.edges()
+            if u != v
+        )
+    H = nx.Graph()
+    H.add_nodes_from(G)
+    H.add_weighted_edges_from((u, v, e) for u, v, e in edges if e != 0)
+    return H
+
+
+def _rcm_estimate(G, nodelist):
+    """Estimate the Fiedler vector using the reverse Cuthill-McKee ordering."""
+    import numpy as np
+
+    G = G.subgraph(nodelist)
+    order = reverse_cuthill_mckee_ordering(G)
+    n = len(nodelist)
+    index = dict(zip(nodelist, range(n)))
+    x = np.ndarray(n, dtype=float)
+    for i, u in enumerate(order):
+        x[index[u]] = i
+    x -= (n - 1) / 2.0
+    return x
+
+
+def _tracemin_fiedler(L, X, normalized, tol, method):
+    """Compute the Fiedler vector of L using the TraceMIN-Fiedler algorithm.
+
+    The Fiedler vector of a connected undirected graph is the eigenvector
+    corresponding to the second smallest eigenvalue of the Laplacian matrix
+    of the graph. This function starts with the Laplacian L, not the Graph.
+
+    Parameters
+    ----------
+    L : Laplacian of a possibly weighted or normalized, but undirected graph
+
+    X : Initial guess for a solution. Usually a matrix of random numbers.
+        This function allows more than one column in X to identify more than
+        one eigenvector if desired.
+
+    normalized : bool
+        Whether the normalized Laplacian matrix is used.
+
+    tol : float
+        Tolerance of relative residual in eigenvalue computation.
+        Warning: There is no limit on number of iterations.
+
+    method : string
+        Should be 'tracemin_pcg' or 'tracemin_lu'.
+        Otherwise exception is raised.
+
+    Returns
+    -------
+    sigma, X : Two NumPy arrays of floats.
+        The lowest eigenvalues and corresponding eigenvectors of L.
+        The size of input X determines the size of these outputs.
+        As this is for Fiedler vectors, the zero eigenvalue (and
+        constant eigenvector) are avoided.
+    """
+    import numpy as np
+    import scipy as sp
+
+    n = X.shape[0]
+
+    if normalized:
+        # Form the normalized Laplacian matrix and determine the eigenvector of
+        # its nullspace.
+        e = np.sqrt(L.diagonal())
+        # TODO: rm csr_array wrapper when spdiags array creation becomes available
+        D = sp.sparse.csr_array(sp.sparse.spdiags(1 / e, 0, n, n, format="csr"))
+        L = D @ L @ D
+        e *= 1.0 / np.linalg.norm(e, 2)
+
+    if normalized:
+
+        def project(X):
+            """Make X orthogonal to the nullspace of L."""
+            X = np.asarray(X)
+            for j in range(X.shape[1]):
+                X[:, j] -= (X[:, j] @ e) * e
+
+    else:
+
+        def project(X):
+            """Make X orthogonal to the nullspace of L."""
+            X = np.asarray(X)
+            for j in range(X.shape[1]):
+                X[:, j] -= X[:, j].sum() / n
+
+    if method == "tracemin_pcg":
+        D = L.diagonal().astype(float)
+        solver = _PCGSolver(lambda x: L @ x, lambda x: D * x)
+    elif method == "tracemin_lu":
+        # Convert A to CSC to suppress SparseEfficiencyWarning.
+        A = sp.sparse.csc_array(L, dtype=float, copy=True)
+        # Force A to be nonsingular. Since A is the Laplacian matrix of a
+        # connected graph, its rank deficiency is one, and thus one diagonal
+        # element needs to modified. Changing to infinity forces a zero in the
+        # corresponding element in the solution.
+        i = (A.indptr[1:] - A.indptr[:-1]).argmax()
+        A[i, i] = np.inf
+        solver = _LUSolver(A)
+    else:
+        raise nx.NetworkXError(f"Unknown linear system solver: {method}")
+
+    # Initialize.
+    Lnorm = abs(L).sum(axis=1).flatten().max()
+    project(X)
+    W = np.ndarray(X.shape, order="F")
+
+    while True:
+        # Orthonormalize X.
+        X = np.linalg.qr(X)[0]
+        # Compute iteration matrix H.
+        W[:, :] = L @ X
+        H = X.T @ W
+        sigma, Y = sp.linalg.eigh(H, overwrite_a=True)
+        # Compute the Ritz vectors.
+        X = X @ Y
+        # Test for convergence exploiting the fact that L * X == W * Y.
+        res = sp.linalg.blas.dasum(W @ Y[:, 0] - sigma[0] * X[:, 0]) / Lnorm
+        if res < tol:
+            break
+        # Compute X = L \ X / (X' * (L \ X)).
+        # L \ X can have an arbitrary projection on the nullspace of L,
+        # which will be eliminated.
+        W[:, :] = solver.solve(X, tol)
+        X = (sp.linalg.inv(W.T @ X) @ W.T).T  # Preserves Fortran storage order.
+        project(X)
+
+    return sigma, np.asarray(X)
+
+
+def _get_fiedler_func(method):
+    """Returns a function that solves the Fiedler eigenvalue problem."""
+    import numpy as np
+
+    if method == "tracemin":  # old style keyword <v2.1
+        method = "tracemin_pcg"
+    if method in ("tracemin_pcg", "tracemin_lu"):
+
+        def find_fiedler(L, x, normalized, tol, seed):
+            q = 1 if method == "tracemin_pcg" else min(4, L.shape[0] - 1)
+            X = np.asarray(seed.normal(size=(q, L.shape[0]))).T
+            sigma, X = _tracemin_fiedler(L, X, normalized, tol, method)
+            return sigma[0], X[:, 0]
+
+    elif method == "lanczos" or method == "lobpcg":
+
+        def find_fiedler(L, x, normalized, tol, seed):
+            import scipy as sp
+
+            L = sp.sparse.csc_array(L, dtype=float)
+            n = L.shape[0]
+            if normalized:
+                # TODO: rm csc_array wrapping when spdiags array becomes available
+                D = sp.sparse.csc_array(
+                    sp.sparse.spdiags(
+                        1.0 / np.sqrt(L.diagonal()), [0], n, n, format="csc"
+                    )
+                )
+                L = D @ L @ D
+            if method == "lanczos" or n < 10:
+                # Avoid LOBPCG when n < 10 due to
+                # https://github.com/scipy/scipy/issues/3592
+                # https://github.com/scipy/scipy/pull/3594
+                sigma, X = sp.sparse.linalg.eigsh(
+                    L, 2, which="SM", tol=tol, return_eigenvectors=True
+                )
+                return sigma[1], X[:, 1]
+            else:
+                X = np.asarray(np.atleast_2d(x).T)
+                # TODO: rm csr_array wrapping when spdiags array becomes available
+                M = sp.sparse.csr_array(sp.sparse.spdiags(1.0 / L.diagonal(), 0, n, n))
+                Y = np.ones(n)
+                if normalized:
+                    Y /= D.diagonal()
+                sigma, X = sp.sparse.linalg.lobpcg(
+                    L, X, M=M, Y=np.atleast_2d(Y).T, tol=tol, maxiter=n, largest=False
+                )
+                return sigma[0], X[:, 0]
+
+    else:
+        raise nx.NetworkXError(f"unknown method {method!r}.")
+
+    return find_fiedler
+
+
+@not_implemented_for("directed")
+@np_random_state(5)
+@nx._dispatchable(edge_attrs="weight")
+def algebraic_connectivity(
+    G, weight="weight", normalized=False, tol=1e-8, method="tracemin_pcg", seed=None
+):
+    r"""Returns the algebraic connectivity of an undirected graph.
+
+    The algebraic connectivity of a connected undirected graph is the second
+    smallest eigenvalue of its Laplacian matrix.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected graph.
+
+    weight : object, optional (default: None)
+        The data key used to determine the weight of each edge. If None, then
+        each edge has unit weight.
+
+    normalized : bool, optional (default: False)
+        Whether the normalized Laplacian matrix is used.
+
+    tol : float, optional (default: 1e-8)
+        Tolerance of relative residual in eigenvalue computation.
+
+    method : string, optional (default: 'tracemin_pcg')
+        Method of eigenvalue computation. It must be one of the tracemin
+        options shown below (TraceMIN), 'lanczos' (Lanczos iteration)
+        or 'lobpcg' (LOBPCG).
+
+        The TraceMIN algorithm uses a linear system solver. The following
+        values allow specifying the solver to be used.
+
+        =============== ========================================
+        Value           Solver
+        =============== ========================================
+        'tracemin_pcg'  Preconditioned conjugate gradient method
+        'tracemin_lu'   LU factorization
+        =============== ========================================
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    algebraic_connectivity : float
+        Algebraic connectivity.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    NetworkXError
+        If G has less than two nodes.
+
+    Notes
+    -----
+    Edge weights are interpreted by their absolute values. For MultiGraph's,
+    weights of parallel edges are summed. Zero-weighted edges are ignored.
+
+    See Also
+    --------
+    laplacian_matrix
+
+    Examples
+    --------
+    For undirected graphs algebraic connectivity can tell us if a graph is connected or not
+    `G` is connected iff  ``algebraic_connectivity(G) > 0``:
+
+    >>> G = nx.complete_graph(5)
+    >>> nx.algebraic_connectivity(G) > 0
+    True
+    >>> G.add_node(10)  # G is no longer connected
+    >>> nx.algebraic_connectivity(G) > 0
+    False
+
+    """
+    if len(G) < 2:
+        raise nx.NetworkXError("graph has less than two nodes.")
+    G = _preprocess_graph(G, weight)
+    if not nx.is_connected(G):
+        return 0.0
+
+    L = nx.laplacian_matrix(G)
+    if L.shape[0] == 2:
+        return 2.0 * float(L[0, 0]) if not normalized else 2.0
+
+    find_fiedler = _get_fiedler_func(method)
+    x = None if method != "lobpcg" else _rcm_estimate(G, G)
+    sigma, fiedler = find_fiedler(L, x, normalized, tol, seed)
+    return float(sigma)
+
+
+@not_implemented_for("directed")
+@np_random_state(5)
+@nx._dispatchable(edge_attrs="weight")
+def fiedler_vector(
+    G, weight="weight", normalized=False, tol=1e-8, method="tracemin_pcg", seed=None
+):
+    """Returns the Fiedler vector of a connected undirected graph.
+
+    The Fiedler vector of a connected undirected graph is the eigenvector
+    corresponding to the second smallest eigenvalue of the Laplacian matrix
+    of the graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected graph.
+
+    weight : object, optional (default: None)
+        The data key used to determine the weight of each edge. If None, then
+        each edge has unit weight.
+
+    normalized : bool, optional (default: False)
+        Whether the normalized Laplacian matrix is used.
+
+    tol : float, optional (default: 1e-8)
+        Tolerance of relative residual in eigenvalue computation.
+
+    method : string, optional (default: 'tracemin_pcg')
+        Method of eigenvalue computation. It must be one of the tracemin
+        options shown below (TraceMIN), 'lanczos' (Lanczos iteration)
+        or 'lobpcg' (LOBPCG).
+
+        The TraceMIN algorithm uses a linear system solver. The following
+        values allow specifying the solver to be used.
+
+        =============== ========================================
+        Value           Solver
+        =============== ========================================
+        'tracemin_pcg'  Preconditioned conjugate gradient method
+        'tracemin_lu'   LU factorization
+        =============== ========================================
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    fiedler_vector : NumPy array of floats.
+        Fiedler vector.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    NetworkXError
+        If G has less than two nodes or is not connected.
+
+    Notes
+    -----
+    Edge weights are interpreted by their absolute values. For MultiGraph's,
+    weights of parallel edges are summed. Zero-weighted edges are ignored.
+
+    See Also
+    --------
+    laplacian_matrix
+
+    Examples
+    --------
+    Given a connected graph the signs of the values in the Fiedler vector can be
+    used to partition the graph into two components.
+
+    >>> G = nx.barbell_graph(5, 0)
+    >>> nx.fiedler_vector(G, normalized=True, seed=1)
+    array([-0.32864129, -0.32864129, -0.32864129, -0.32864129, -0.26072899,
+            0.26072899,  0.32864129,  0.32864129,  0.32864129,  0.32864129])
+
+    The connected components are the two 5-node cliques of the barbell graph.
+    """
+    import numpy as np
+
+    if len(G) < 2:
+        raise nx.NetworkXError("graph has less than two nodes.")
+    G = _preprocess_graph(G, weight)
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("graph is not connected.")
+
+    if len(G) == 2:
+        return np.array([1.0, -1.0])
+
+    find_fiedler = _get_fiedler_func(method)
+    L = nx.laplacian_matrix(G)
+    x = None if method != "lobpcg" else _rcm_estimate(G, G)
+    sigma, fiedler = find_fiedler(L, x, normalized, tol, seed)
+    return fiedler
+
+
+@np_random_state(5)
+@nx._dispatchable(edge_attrs="weight")
+def spectral_ordering(
+    G, weight="weight", normalized=False, tol=1e-8, method="tracemin_pcg", seed=None
+):
+    """Compute the spectral_ordering of a graph.
+
+    The spectral ordering of a graph is an ordering of its nodes where nodes
+    in the same weakly connected components appear contiguous and ordered by
+    their corresponding elements in the Fiedler vector of the component.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A graph.
+
+    weight : object, optional (default: None)
+        The data key used to determine the weight of each edge. If None, then
+        each edge has unit weight.
+
+    normalized : bool, optional (default: False)
+        Whether the normalized Laplacian matrix is used.
+
+    tol : float, optional (default: 1e-8)
+        Tolerance of relative residual in eigenvalue computation.
+
+    method : string, optional (default: 'tracemin_pcg')
+        Method of eigenvalue computation. It must be one of the tracemin
+        options shown below (TraceMIN), 'lanczos' (Lanczos iteration)
+        or 'lobpcg' (LOBPCG).
+
+        The TraceMIN algorithm uses a linear system solver. The following
+        values allow specifying the solver to be used.
+
+        =============== ========================================
+        Value           Solver
+        =============== ========================================
+        'tracemin_pcg'  Preconditioned conjugate gradient method
+        'tracemin_lu'   LU factorization
+        =============== ========================================
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    spectral_ordering : NumPy array of floats.
+        Spectral ordering of nodes.
+
+    Raises
+    ------
+    NetworkXError
+        If G is empty.
+
+    Notes
+    -----
+    Edge weights are interpreted by their absolute values. For MultiGraph's,
+    weights of parallel edges are summed. Zero-weighted edges are ignored.
+
+    See Also
+    --------
+    laplacian_matrix
+    """
+    if len(G) == 0:
+        raise nx.NetworkXError("graph is empty.")
+    G = _preprocess_graph(G, weight)
+
+    find_fiedler = _get_fiedler_func(method)
+    order = []
+    for component in nx.connected_components(G):
+        size = len(component)
+        if size > 2:
+            L = nx.laplacian_matrix(G, component)
+            x = None if method != "lobpcg" else _rcm_estimate(G, component)
+            sigma, fiedler = find_fiedler(L, x, normalized, tol, seed)
+            sort_info = zip(fiedler, range(size), component)
+            order.extend(u for x, c, u in sorted(sort_info))
+        else:
+            order.extend(component)
+
+    return order
+
+
+@nx._dispatchable(edge_attrs="weight")
+def spectral_bisection(
+    G, weight="weight", normalized=False, tol=1e-8, method="tracemin_pcg", seed=None
+):
+    """Bisect the graph using the Fiedler vector.
+
+    This method uses the Fiedler vector to bisect a graph.
+    The partition is defined by the nodes which are associated with
+    either positive or negative values in the vector.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    weight : str, optional (default: weight)
+        The data key used to determine the weight of each edge. If None, then
+        each edge has unit weight.
+
+    normalized : bool, optional (default: False)
+        Whether the normalized Laplacian matrix is used.
+
+    tol : float, optional (default: 1e-8)
+        Tolerance of relative residual in eigenvalue computation.
+
+    method : string, optional (default: 'tracemin_pcg')
+        Method of eigenvalue computation. It must be one of the tracemin
+        options shown below (TraceMIN), 'lanczos' (Lanczos iteration)
+        or 'lobpcg' (LOBPCG).
+
+        The TraceMIN algorithm uses a linear system solver. The following
+        values allow specifying the solver to be used.
+
+        =============== ========================================
+        Value           Solver
+        =============== ========================================
+        'tracemin_pcg'  Preconditioned conjugate gradient method
+        'tracemin_lu'   LU factorization
+        =============== ========================================
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    bisection : tuple of sets
+        Sets with the bisection of nodes
+
+    Examples
+    --------
+    >>> G = nx.barbell_graph(3, 0)
+    >>> nx.spectral_bisection(G)
+    ({0, 1, 2}, {3, 4, 5})
+
+    References
+    ----------
+    .. [1] M. E. J Newman 'Networks: An Introduction', pages 364-370
+       Oxford University Press 2011.
+    """
+    import numpy as np
+
+    v = nx.fiedler_vector(G, weight, normalized, tol, method, seed)
+    nodes = np.array(list(G))
+    pos_vals = v >= 0
+
+    return set(nodes[~pos_vals].tolist()), set(nodes[pos_vals].tolist())
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/attrmatrix.py b/.venv/lib/python3.12/site-packages/networkx/linalg/attrmatrix.py
new file mode 100644
index 00000000..b5a70492
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/attrmatrix.py
@@ -0,0 +1,465 @@
+"""
+Functions for constructing matrix-like objects from graph attributes.
+"""
+
+import networkx as nx
+
+__all__ = ["attr_matrix", "attr_sparse_matrix"]
+
+
+def _node_value(G, node_attr):
+    """Returns a function that returns a value from G.nodes[u].
+
+    We return a function expecting a node as its sole argument. Then, in the
+    simplest scenario, the returned function will return G.nodes[u][node_attr].
+    However, we also handle the case when `node_attr` is None or when it is a
+    function itself.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph
+
+    node_attr : {None, str, callable}
+        Specification of how the value of the node attribute should be obtained
+        from the node attribute dictionary.
+
+    Returns
+    -------
+    value : function
+        A function expecting a node as its sole argument. The function will
+        returns a value from G.nodes[u] that depends on `edge_attr`.
+
+    """
+    if node_attr is None:
+
+        def value(u):
+            return u
+
+    elif not callable(node_attr):
+        # assume it is a key for the node attribute dictionary
+        def value(u):
+            return G.nodes[u][node_attr]
+
+    else:
+        # Advanced:  Allow users to specify something else.
+        #
+        # For example,
+        #     node_attr = lambda u: G.nodes[u].get('size', .5) * 3
+        #
+        value = node_attr
+
+    return value
+
+
+def _edge_value(G, edge_attr):
+    """Returns a function that returns a value from G[u][v].
+
+    Suppose there exists an edge between u and v.  Then we return a function
+    expecting u and v as arguments.  For Graph and DiGraph, G[u][v] is
+    the edge attribute dictionary, and the function (essentially) returns
+    G[u][v][edge_attr].  However, we also handle cases when `edge_attr` is None
+    and when it is a function itself. For MultiGraph and MultiDiGraph, G[u][v]
+    is a dictionary of all edges between u and v.  In this case, the returned
+    function sums the value of `edge_attr` for every edge between u and v.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    edge_attr : {None, str, callable}
+        Specification of how the value of the edge attribute should be obtained
+        from the edge attribute dictionary, G[u][v].  For multigraphs, G[u][v]
+        is a dictionary of all the edges between u and v.  This allows for
+        special treatment of multiedges.
+
+    Returns
+    -------
+    value : function
+        A function expecting two nodes as parameters. The nodes should
+        represent the from- and to- node of an edge. The function will
+        return a value from G[u][v] that depends on `edge_attr`.
+
+    """
+
+    if edge_attr is None:
+        # topological count of edges
+
+        if G.is_multigraph():
+
+            def value(u, v):
+                return len(G[u][v])
+
+        else:
+
+            def value(u, v):
+                return 1
+
+    elif not callable(edge_attr):
+        # assume it is a key for the edge attribute dictionary
+
+        if edge_attr == "weight":
+            # provide a default value
+            if G.is_multigraph():
+
+                def value(u, v):
+                    return sum(d.get(edge_attr, 1) for d in G[u][v].values())
+
+            else:
+
+                def value(u, v):
+                    return G[u][v].get(edge_attr, 1)
+
+        else:
+            # otherwise, the edge attribute MUST exist for each edge
+            if G.is_multigraph():
+
+                def value(u, v):
+                    return sum(d[edge_attr] for d in G[u][v].values())
+
+            else:
+
+                def value(u, v):
+                    return G[u][v][edge_attr]
+
+    else:
+        # Advanced:  Allow users to specify something else.
+        #
+        # Alternative default value:
+        #     edge_attr = lambda u,v: G[u][v].get('thickness', .5)
+        #
+        # Function on an attribute:
+        #     edge_attr = lambda u,v: abs(G[u][v]['weight'])
+        #
+        # Handle Multi(Di)Graphs differently:
+        #     edge_attr = lambda u,v: numpy.prod([d['size'] for d in G[u][v].values()])
+        #
+        # Ignore multiple edges
+        #     edge_attr = lambda u,v: 1 if len(G[u][v]) else 0
+        #
+        value = edge_attr
+
+    return value
+
+
+@nx._dispatchable(edge_attrs={"edge_attr": None}, node_attrs="node_attr")
+def attr_matrix(
+    G,
+    edge_attr=None,
+    node_attr=None,
+    normalized=False,
+    rc_order=None,
+    dtype=None,
+    order=None,
+):
+    """Returns the attribute matrix using attributes from `G` as a numpy array.
+
+    If only `G` is passed in, then the adjacency matrix is constructed.
+
+    Let A be a discrete set of values for the node attribute `node_attr`. Then
+    the elements of A represent the rows and columns of the constructed matrix.
+    Now, iterate through every edge e=(u,v) in `G` and consider the value
+    of the edge attribute `edge_attr`.  If ua and va are the values of the
+    node attribute `node_attr` for u and v, respectively, then the value of
+    the edge attribute is added to the matrix element at (ua, va).
+
+    Parameters
+    ----------
+    G : graph
+        The NetworkX graph used to construct the attribute matrix.
+
+    edge_attr : str, optional
+        Each element of the matrix represents a running total of the
+        specified edge attribute for edges whose node attributes correspond
+        to the rows/cols of the matrix. The attribute must be present for
+        all edges in the graph. If no attribute is specified, then we
+        just count the number of edges whose node attributes correspond
+        to the matrix element.
+
+    node_attr : str, optional
+        Each row and column in the matrix represents a particular value
+        of the node attribute.  The attribute must be present for all nodes
+        in the graph. Note, the values of this attribute should be reliably
+        hashable. So, float values are not recommended. If no attribute is
+        specified, then the rows and columns will be the nodes of the graph.
+
+    normalized : bool, optional
+        If True, then each row is normalized by the summation of its values.
+
+    rc_order : list, optional
+        A list of the node attribute values. This list specifies the ordering
+        of rows and columns of the array. If no ordering is provided, then
+        the ordering will be random (and also, a return value).
+
+    Other Parameters
+    ----------------
+    dtype : NumPy data-type, optional
+        A valid NumPy dtype used to initialize the array. Keep in mind certain
+        dtypes can yield unexpected results if the array is to be normalized.
+        The parameter is passed to numpy.zeros(). If unspecified, the NumPy
+        default is used.
+
+    order : {'C', 'F'}, optional
+        Whether to store multidimensional data in C- or Fortran-contiguous
+        (row- or column-wise) order in memory. This parameter is passed to
+        numpy.zeros(). If unspecified, the NumPy default is used.
+
+    Returns
+    -------
+    M : 2D NumPy ndarray
+        The attribute matrix.
+
+    ordering : list
+        If `rc_order` was specified, then only the attribute matrix is returned.
+        However, if `rc_order` was None, then the ordering used to construct
+        the matrix is returned as well.
+
+    Examples
+    --------
+    Construct an adjacency matrix:
+
+    >>> G = nx.Graph()
+    >>> G.add_edge(0, 1, thickness=1, weight=3)
+    >>> G.add_edge(0, 2, thickness=2)
+    >>> G.add_edge(1, 2, thickness=3)
+    >>> nx.attr_matrix(G, rc_order=[0, 1, 2])
+    array([[0., 1., 1.],
+           [1., 0., 1.],
+           [1., 1., 0.]])
+
+    Alternatively, we can obtain the matrix describing edge thickness.
+
+    >>> nx.attr_matrix(G, edge_attr="thickness", rc_order=[0, 1, 2])
+    array([[0., 1., 2.],
+           [1., 0., 3.],
+           [2., 3., 0.]])
+
+    We can also color the nodes and ask for the probability distribution over
+    all edges (u,v) describing:
+
+        Pr(v has color Y | u has color X)
+
+    >>> G.nodes[0]["color"] = "red"
+    >>> G.nodes[1]["color"] = "red"
+    >>> G.nodes[2]["color"] = "blue"
+    >>> rc = ["red", "blue"]
+    >>> nx.attr_matrix(G, node_attr="color", normalized=True, rc_order=rc)
+    array([[0.33333333, 0.66666667],
+           [1.        , 0.        ]])
+
+    For example, the above tells us that for all edges (u,v):
+
+        Pr( v is red  | u is red)  = 1/3
+        Pr( v is blue | u is red)  = 2/3
+
+        Pr( v is red  | u is blue) = 1
+        Pr( v is blue | u is blue) = 0
+
+    Finally, we can obtain the total weights listed by the node colors.
+
+    >>> nx.attr_matrix(G, edge_attr="weight", node_attr="color", rc_order=rc)
+    array([[3., 2.],
+           [2., 0.]])
+
+    Thus, the total weight over all edges (u,v) with u and v having colors:
+
+        (red, red)   is 3   # the sole contribution is from edge (0,1)
+        (red, blue)  is 2   # contributions from edges (0,2) and (1,2)
+        (blue, red)  is 2   # same as (red, blue) since graph is undirected
+        (blue, blue) is 0   # there are no edges with blue endpoints
+
+    """
+    import numpy as np
+
+    edge_value = _edge_value(G, edge_attr)
+    node_value = _node_value(G, node_attr)
+
+    if rc_order is None:
+        ordering = list({node_value(n) for n in G})
+    else:
+        ordering = rc_order
+
+    N = len(ordering)
+    undirected = not G.is_directed()
+    index = dict(zip(ordering, range(N)))
+    M = np.zeros((N, N), dtype=dtype, order=order)
+
+    seen = set()
+    for u, nbrdict in G.adjacency():
+        for v in nbrdict:
+            # Obtain the node attribute values.
+            i, j = index[node_value(u)], index[node_value(v)]
+            if v not in seen:
+                M[i, j] += edge_value(u, v)
+                if undirected:
+                    M[j, i] = M[i, j]
+
+        if undirected:
+            seen.add(u)
+
+    if normalized:
+        M /= M.sum(axis=1).reshape((N, 1))
+
+    if rc_order is None:
+        return M, ordering
+    else:
+        return M
+
+
+@nx._dispatchable(edge_attrs={"edge_attr": None}, node_attrs="node_attr")
+def attr_sparse_matrix(
+    G, edge_attr=None, node_attr=None, normalized=False, rc_order=None, dtype=None
+):
+    """Returns a SciPy sparse array using attributes from G.
+
+    If only `G` is passed in, then the adjacency matrix is constructed.
+
+    Let A be a discrete set of values for the node attribute `node_attr`. Then
+    the elements of A represent the rows and columns of the constructed matrix.
+    Now, iterate through every edge e=(u,v) in `G` and consider the value
+    of the edge attribute `edge_attr`.  If ua and va are the values of the
+    node attribute `node_attr` for u and v, respectively, then the value of
+    the edge attribute is added to the matrix element at (ua, va).
+
+    Parameters
+    ----------
+    G : graph
+        The NetworkX graph used to construct the NumPy matrix.
+
+    edge_attr : str, optional
+        Each element of the matrix represents a running total of the
+        specified edge attribute for edges whose node attributes correspond
+        to the rows/cols of the matrix. The attribute must be present for
+        all edges in the graph. If no attribute is specified, then we
+        just count the number of edges whose node attributes correspond
+        to the matrix element.
+
+    node_attr : str, optional
+        Each row and column in the matrix represents a particular value
+        of the node attribute.  The attribute must be present for all nodes
+        in the graph. Note, the values of this attribute should be reliably
+        hashable. So, float values are not recommended. If no attribute is
+        specified, then the rows and columns will be the nodes of the graph.
+
+    normalized : bool, optional
+        If True, then each row is normalized by the summation of its values.
+
+    rc_order : list, optional
+        A list of the node attribute values. This list specifies the ordering
+        of rows and columns of the array. If no ordering is provided, then
+        the ordering will be random (and also, a return value).
+
+    Other Parameters
+    ----------------
+    dtype : NumPy data-type, optional
+        A valid NumPy dtype used to initialize the array. Keep in mind certain
+        dtypes can yield unexpected results if the array is to be normalized.
+        The parameter is passed to numpy.zeros(). If unspecified, the NumPy
+        default is used.
+
+    Returns
+    -------
+    M : SciPy sparse array
+        The attribute matrix.
+
+    ordering : list
+        If `rc_order` was specified, then only the matrix is returned.
+        However, if `rc_order` was None, then the ordering used to construct
+        the matrix is returned as well.
+
+    Examples
+    --------
+    Construct an adjacency matrix:
+
+    >>> G = nx.Graph()
+    >>> G.add_edge(0, 1, thickness=1, weight=3)
+    >>> G.add_edge(0, 2, thickness=2)
+    >>> G.add_edge(1, 2, thickness=3)
+    >>> M = nx.attr_sparse_matrix(G, rc_order=[0, 1, 2])
+    >>> M.toarray()
+    array([[0., 1., 1.],
+           [1., 0., 1.],
+           [1., 1., 0.]])
+
+    Alternatively, we can obtain the matrix describing edge thickness.
+
+    >>> M = nx.attr_sparse_matrix(G, edge_attr="thickness", rc_order=[0, 1, 2])
+    >>> M.toarray()
+    array([[0., 1., 2.],
+           [1., 0., 3.],
+           [2., 3., 0.]])
+
+    We can also color the nodes and ask for the probability distribution over
+    all edges (u,v) describing:
+
+        Pr(v has color Y | u has color X)
+
+    >>> G.nodes[0]["color"] = "red"
+    >>> G.nodes[1]["color"] = "red"
+    >>> G.nodes[2]["color"] = "blue"
+    >>> rc = ["red", "blue"]
+    >>> M = nx.attr_sparse_matrix(G, node_attr="color", normalized=True, rc_order=rc)
+    >>> M.toarray()
+    array([[0.33333333, 0.66666667],
+           [1.        , 0.        ]])
+
+    For example, the above tells us that for all edges (u,v):
+
+        Pr( v is red  | u is red)  = 1/3
+        Pr( v is blue | u is red)  = 2/3
+
+        Pr( v is red  | u is blue) = 1
+        Pr( v is blue | u is blue) = 0
+
+    Finally, we can obtain the total weights listed by the node colors.
+
+    >>> M = nx.attr_sparse_matrix(G, edge_attr="weight", node_attr="color", rc_order=rc)
+    >>> M.toarray()
+    array([[3., 2.],
+           [2., 0.]])
+
+    Thus, the total weight over all edges (u,v) with u and v having colors:
+
+        (red, red)   is 3   # the sole contribution is from edge (0,1)
+        (red, blue)  is 2   # contributions from edges (0,2) and (1,2)
+        (blue, red)  is 2   # same as (red, blue) since graph is undirected
+        (blue, blue) is 0   # there are no edges with blue endpoints
+
+    """
+    import numpy as np
+    import scipy as sp
+
+    edge_value = _edge_value(G, edge_attr)
+    node_value = _node_value(G, node_attr)
+
+    if rc_order is None:
+        ordering = list({node_value(n) for n in G})
+    else:
+        ordering = rc_order
+
+    N = len(ordering)
+    undirected = not G.is_directed()
+    index = dict(zip(ordering, range(N)))
+    M = sp.sparse.lil_array((N, N), dtype=dtype)
+
+    seen = set()
+    for u, nbrdict in G.adjacency():
+        for v in nbrdict:
+            # Obtain the node attribute values.
+            i, j = index[node_value(u)], index[node_value(v)]
+            if v not in seen:
+                M[i, j] += edge_value(u, v)
+                if undirected:
+                    M[j, i] = M[i, j]
+
+        if undirected:
+            seen.add(u)
+
+    if normalized:
+        M *= 1 / M.sum(axis=1)[:, np.newaxis]  # in-place mult preserves sparse
+
+    if rc_order is None:
+        return M, ordering
+    else:
+        return M
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/bethehessianmatrix.py b/.venv/lib/python3.12/site-packages/networkx/linalg/bethehessianmatrix.py
new file mode 100644
index 00000000..3d42fc6d
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/bethehessianmatrix.py
@@ -0,0 +1,79 @@
+"""Bethe Hessian or deformed Laplacian matrix of graphs."""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["bethe_hessian_matrix"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def bethe_hessian_matrix(G, r=None, nodelist=None):
+    r"""Returns the Bethe Hessian matrix of G.
+
+    The Bethe Hessian is a family of matrices parametrized by r, defined as
+    H(r) = (r^2 - 1) I - r A + D where A is the adjacency matrix, D is the
+    diagonal matrix of node degrees, and I is the identify matrix. It is equal
+    to the graph laplacian when the regularizer r = 1.
+
+    The default choice of regularizer should be the ratio [2]_
+
+    .. math::
+      r_m = \left(\sum k_i \right)^{-1}\left(\sum k_i^2 \right) - 1
+
+    Parameters
+    ----------
+    G : Graph
+       A NetworkX graph
+    r : float
+       Regularizer parameter
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by ``G.nodes()``.
+
+    Returns
+    -------
+    H : scipy.sparse.csr_array
+      The Bethe Hessian matrix of `G`, with parameter `r`.
+
+    Examples
+    --------
+    >>> k = [3, 2, 2, 1, 0]
+    >>> G = nx.havel_hakimi_graph(k)
+    >>> H = nx.bethe_hessian_matrix(G)
+    >>> H.toarray()
+    array([[ 3.5625, -1.25  , -1.25  , -1.25  ,  0.    ],
+           [-1.25  ,  2.5625, -1.25  ,  0.    ,  0.    ],
+           [-1.25  , -1.25  ,  2.5625,  0.    ,  0.    ],
+           [-1.25  ,  0.    ,  0.    ,  1.5625,  0.    ],
+           [ 0.    ,  0.    ,  0.    ,  0.    ,  0.5625]])
+
+    See Also
+    --------
+    bethe_hessian_spectrum
+    adjacency_matrix
+    laplacian_matrix
+
+    References
+    ----------
+    .. [1] A. Saade, F. Krzakala and L. Zdeborová
+       "Spectral Clustering of Graphs with the Bethe Hessian",
+       Advances in Neural Information Processing Systems, 2014.
+    .. [2] C. M. Le, E. Levina
+       "Estimating the number of communities in networks by spectral methods"
+       arXiv:1507.00827, 2015.
+    """
+    import scipy as sp
+
+    if nodelist is None:
+        nodelist = list(G)
+    if r is None:
+        r = sum(d**2 for v, d in nx.degree(G)) / sum(d for v, d in nx.degree(G)) - 1
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, format="csr")
+    n, m = A.shape
+    # TODO: Rm csr_array wrapper when spdiags array creation becomes available
+    D = sp.sparse.csr_array(sp.sparse.spdiags(A.sum(axis=1), 0, m, n, format="csr"))
+    # TODO: Rm csr_array wrapper when eye array creation becomes available
+    I = sp.sparse.csr_array(sp.sparse.eye(m, n, format="csr"))
+    return (r**2 - 1) * I - r * A + D
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/graphmatrix.py b/.venv/lib/python3.12/site-packages/networkx/linalg/graphmatrix.py
new file mode 100644
index 00000000..9f477bcc
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/graphmatrix.py
@@ -0,0 +1,168 @@
+"""
+Adjacency matrix and incidence matrix of graphs.
+"""
+
+import networkx as nx
+
+__all__ = ["incidence_matrix", "adjacency_matrix"]
+
+
+@nx._dispatchable(edge_attrs="weight")
+def incidence_matrix(
+    G, nodelist=None, edgelist=None, oriented=False, weight=None, *, dtype=None
+):
+    """Returns incidence matrix of G.
+
+    The incidence matrix assigns each row to a node and each column to an edge.
+    For a standard incidence matrix a 1 appears wherever a row's node is
+    incident on the column's edge.  For an oriented incidence matrix each
+    edge is assigned an orientation (arbitrarily for undirected and aligning to
+    direction for directed).  A -1 appears for the source (tail) of an edge and
+    1 for the destination (head) of the edge.  The elements are zero otherwise.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    nodelist : list, optional   (default= all nodes in G)
+       The rows are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    edgelist : list, optional (default= all edges in G)
+       The columns are ordered according to the edges in edgelist.
+       If edgelist is None, then the ordering is produced by G.edges().
+
+    oriented: bool, optional (default=False)
+       If True, matrix elements are +1 or -1 for the head or tail node
+       respectively of each edge.  If False, +1 occurs at both nodes.
+
+    weight : string or None, optional (default=None)
+       The edge data key used to provide each value in the matrix.
+       If None, then each edge has weight 1.  Edge weights, if used,
+       should be positive so that the orientation can provide the sign.
+
+    dtype : a NumPy dtype or None (default=None)
+        The dtype of the output sparse array. This type should be a compatible
+        type of the weight argument, eg. if weight would return a float this
+        argument should also be a float.
+        If None, then the default for SciPy is used.
+
+    Returns
+    -------
+    A : SciPy sparse array
+      The incidence matrix of G.
+
+    Notes
+    -----
+    For MultiGraph/MultiDiGraph, the edges in edgelist should be
+    (u,v,key) 3-tuples.
+
+    "Networks are the best discrete model for so many problems in
+    applied mathematics" [1]_.
+
+    References
+    ----------
+    .. [1] Gil Strang, Network applications: A = incidence matrix,
+       http://videolectures.net/mit18085f07_strang_lec03/
+    """
+    import scipy as sp
+
+    if nodelist is None:
+        nodelist = list(G)
+    if edgelist is None:
+        if G.is_multigraph():
+            edgelist = list(G.edges(keys=True))
+        else:
+            edgelist = list(G.edges())
+    A = sp.sparse.lil_array((len(nodelist), len(edgelist)), dtype=dtype)
+    node_index = {node: i for i, node in enumerate(nodelist)}
+    for ei, e in enumerate(edgelist):
+        (u, v) = e[:2]
+        if u == v:
+            continue  # self loops give zero column
+        try:
+            ui = node_index[u]
+            vi = node_index[v]
+        except KeyError as err:
+            raise nx.NetworkXError(
+                f"node {u} or {v} in edgelist but not in nodelist"
+            ) from err
+        if weight is None:
+            wt = 1
+        else:
+            if G.is_multigraph():
+                ekey = e[2]
+                wt = G[u][v][ekey].get(weight, 1)
+            else:
+                wt = G[u][v].get(weight, 1)
+        if oriented:
+            A[ui, ei] = -wt
+            A[vi, ei] = wt
+        else:
+            A[ui, ei] = wt
+            A[vi, ei] = wt
+    return A.asformat("csc")
+
+
+@nx._dispatchable(edge_attrs="weight")
+def adjacency_matrix(G, nodelist=None, dtype=None, weight="weight"):
+    """Returns adjacency matrix of `G`.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in `nodelist`.
+       If ``nodelist=None`` (the default), then the ordering is produced by
+       ``G.nodes()``.
+
+    dtype : NumPy data-type, optional
+        The desired data-type for the array.
+        If `None`, then the NumPy default is used.
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to provide each value in the matrix.
+       If None, then each edge has weight 1.
+
+    Returns
+    -------
+    A : SciPy sparse array
+      Adjacency matrix representation of G.
+
+    Notes
+    -----
+    For directed graphs, entry ``i, j`` corresponds to an edge from ``i`` to ``j``.
+
+    If you want a pure Python adjacency matrix representation try
+    :func:`~networkx.convert.to_dict_of_dicts` which will return a
+    dictionary-of-dictionaries format that can be addressed as a
+    sparse matrix.
+
+    For multigraphs with parallel edges the weights are summed.
+    See :func:`networkx.convert_matrix.to_numpy_array` for other options.
+
+    The convention used for self-loop edges in graphs is to assign the
+    diagonal matrix entry value to the edge weight attribute
+    (or the number 1 if the edge has no weight attribute).  If the
+    alternate convention of doubling the edge weight is desired the
+    resulting SciPy sparse array can be modified as follows::
+
+        >>> G = nx.Graph([(1, 1)])
+        >>> A = nx.adjacency_matrix(G)
+        >>> A.toarray()
+        array([[1]])
+        >>> A.setdiag(A.diagonal() * 2)
+        >>> A.toarray()
+        array([[2]])
+
+    See Also
+    --------
+    to_numpy_array
+    to_scipy_sparse_array
+    to_dict_of_dicts
+    adjacency_spectrum
+    """
+    return nx.to_scipy_sparse_array(G, nodelist=nodelist, dtype=dtype, weight=weight)
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/laplacianmatrix.py b/.venv/lib/python3.12/site-packages/networkx/linalg/laplacianmatrix.py
new file mode 100644
index 00000000..d49ae491
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/laplacianmatrix.py
@@ -0,0 +1,617 @@
+"""Laplacian matrix of graphs.
+
+All calculations here are done using the out-degree. For Laplacians using
+in-degree, use `G.reverse(copy=False)` instead of `G` and take the transpose.
+
+The `laplacian_matrix` function provides an unnormalized matrix,
+while `normalized_laplacian_matrix`, `directed_laplacian_matrix`,
+and `directed_combinatorial_laplacian_matrix` are all normalized.
+"""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = [
+    "laplacian_matrix",
+    "normalized_laplacian_matrix",
+    "total_spanning_tree_weight",
+    "directed_laplacian_matrix",
+    "directed_combinatorial_laplacian_matrix",
+]
+
+
+@nx._dispatchable(edge_attrs="weight")
+def laplacian_matrix(G, nodelist=None, weight="weight"):
+    """Returns the Laplacian matrix of G.
+
+    The graph Laplacian is the matrix L = D - A, where
+    A is the adjacency matrix and D is the diagonal matrix of node degrees.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    Returns
+    -------
+    L : SciPy sparse array
+      The Laplacian matrix of G.
+
+    Notes
+    -----
+    For MultiGraph, the edges weights are summed.
+
+    This returns an unnormalized matrix. For a normalized output,
+    use `normalized_laplacian_matrix`, `directed_laplacian_matrix`,
+    or `directed_combinatorial_laplacian_matrix`.
+
+    This calculation uses the out-degree of the graph `G`. To use the
+    in-degree for calculations instead, use `G.reverse(copy=False)` and
+    take the transpose.
+
+    See Also
+    --------
+    :func:`~networkx.convert_matrix.to_numpy_array`
+    normalized_laplacian_matrix
+    directed_laplacian_matrix
+    directed_combinatorial_laplacian_matrix
+    :func:`~networkx.linalg.spectrum.laplacian_spectrum`
+
+    Examples
+    --------
+    For graphs with multiple connected components, L is permutation-similar
+    to a block diagonal matrix where each block is the respective Laplacian
+    matrix for each component.
+
+    >>> G = nx.Graph([(1, 2), (2, 3), (4, 5)])
+    >>> print(nx.laplacian_matrix(G).toarray())
+    [[ 1 -1  0  0  0]
+     [-1  2 -1  0  0]
+     [ 0 -1  1  0  0]
+     [ 0  0  0  1 -1]
+     [ 0  0  0 -1  1]]
+
+    >>> edges = [
+    ...     (1, 2),
+    ...     (2, 1),
+    ...     (2, 4),
+    ...     (4, 3),
+    ...     (3, 4),
+    ... ]
+    >>> DiG = nx.DiGraph(edges)
+    >>> print(nx.laplacian_matrix(DiG).toarray())
+    [[ 1 -1  0  0]
+     [-1  2 -1  0]
+     [ 0  0  1 -1]
+     [ 0  0 -1  1]]
+
+    Notice that node 4 is represented by the third column and row. This is because
+    by default the row/column order is the order of `G.nodes` (i.e. the node added
+    order -- in the edgelist, 4 first appears in (2, 4), before node 3 in edge (4, 3).)
+    To control the node order of the matrix, use the `nodelist` argument.
+
+    >>> print(nx.laplacian_matrix(DiG, nodelist=[1, 2, 3, 4]).toarray())
+    [[ 1 -1  0  0]
+     [-1  2  0 -1]
+     [ 0  0  1 -1]
+     [ 0  0 -1  1]]
+
+    This calculation uses the out-degree of the graph `G`. To use the
+    in-degree for calculations instead, use `G.reverse(copy=False)` and
+    take the transpose.
+
+    >>> print(nx.laplacian_matrix(DiG.reverse(copy=False)).toarray().T)
+    [[ 1 -1  0  0]
+     [-1  1 -1  0]
+     [ 0  0  2 -1]
+     [ 0  0 -1  1]]
+
+    References
+    ----------
+    .. [1] Langville, Amy N., and Carl D. Meyer. Google’s PageRank and Beyond:
+       The Science of Search Engine Rankings. Princeton University Press, 2006.
+
+    """
+    import scipy as sp
+
+    if nodelist is None:
+        nodelist = list(G)
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, format="csr")
+    n, m = A.shape
+    # TODO: rm csr_array wrapper when spdiags can produce arrays
+    D = sp.sparse.csr_array(sp.sparse.spdiags(A.sum(axis=1), 0, m, n, format="csr"))
+    return D - A
+
+
+@nx._dispatchable(edge_attrs="weight")
+def normalized_laplacian_matrix(G, nodelist=None, weight="weight"):
+    r"""Returns the normalized Laplacian matrix of G.
+
+    The normalized graph Laplacian is the matrix
+
+    .. math::
+
+        N = D^{-1/2} L D^{-1/2}
+
+    where `L` is the graph Laplacian and `D` is the diagonal matrix of
+    node degrees [1]_.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    Returns
+    -------
+    N : SciPy sparse array
+      The normalized Laplacian matrix of G.
+
+    Notes
+    -----
+    For MultiGraph, the edges weights are summed.
+    See :func:`to_numpy_array` for other options.
+
+    If the Graph contains selfloops, D is defined as ``diag(sum(A, 1))``, where A is
+    the adjacency matrix [2]_.
+
+    This calculation uses the out-degree of the graph `G`. To use the
+    in-degree for calculations instead, use `G.reverse(copy=False)` and
+    take the transpose.
+
+    For an unnormalized output, use `laplacian_matrix`.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> edges = [
+    ...     (1, 2),
+    ...     (2, 1),
+    ...     (2, 4),
+    ...     (4, 3),
+    ...     (3, 4),
+    ... ]
+    >>> DiG = nx.DiGraph(edges)
+    >>> print(nx.normalized_laplacian_matrix(DiG).toarray())
+    [[ 1.         -0.70710678  0.          0.        ]
+     [-0.70710678  1.         -0.70710678  0.        ]
+     [ 0.          0.          1.         -1.        ]
+     [ 0.          0.         -1.          1.        ]]
+
+    Notice that node 4 is represented by the third column and row. This is because
+    by default the row/column order is the order of `G.nodes` (i.e. the node added
+    order -- in the edgelist, 4 first appears in (2, 4), before node 3 in edge (4, 3).)
+    To control the node order of the matrix, use the `nodelist` argument.
+
+    >>> print(nx.normalized_laplacian_matrix(DiG, nodelist=[1, 2, 3, 4]).toarray())
+    [[ 1.         -0.70710678  0.          0.        ]
+     [-0.70710678  1.          0.         -0.70710678]
+     [ 0.          0.          1.         -1.        ]
+     [ 0.          0.         -1.          1.        ]]
+    >>> G = nx.Graph(edges)
+    >>> print(nx.normalized_laplacian_matrix(G).toarray())
+    [[ 1.         -0.70710678  0.          0.        ]
+     [-0.70710678  1.         -0.5         0.        ]
+     [ 0.         -0.5         1.         -0.70710678]
+     [ 0.          0.         -0.70710678  1.        ]]
+
+    See Also
+    --------
+    laplacian_matrix
+    normalized_laplacian_spectrum
+    directed_laplacian_matrix
+    directed_combinatorial_laplacian_matrix
+
+    References
+    ----------
+    .. [1] Fan Chung-Graham, Spectral Graph Theory,
+       CBMS Regional Conference Series in Mathematics, Number 92, 1997.
+    .. [2] Steve Butler, Interlacing For Weighted Graphs Using The Normalized
+       Laplacian, Electronic Journal of Linear Algebra, Volume 16, pp. 90-98,
+       March 2007.
+    .. [3] Langville, Amy N., and Carl D. Meyer. Google’s PageRank and Beyond:
+       The Science of Search Engine Rankings. Princeton University Press, 2006.
+    """
+    import numpy as np
+    import scipy as sp
+
+    if nodelist is None:
+        nodelist = list(G)
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, format="csr")
+    n, _ = A.shape
+    diags = A.sum(axis=1)
+    # TODO: rm csr_array wrapper when spdiags can produce arrays
+    D = sp.sparse.csr_array(sp.sparse.spdiags(diags, 0, n, n, format="csr"))
+    L = D - A
+    with np.errstate(divide="ignore"):
+        diags_sqrt = 1.0 / np.sqrt(diags)
+    diags_sqrt[np.isinf(diags_sqrt)] = 0
+    # TODO: rm csr_array wrapper when spdiags can produce arrays
+    DH = sp.sparse.csr_array(sp.sparse.spdiags(diags_sqrt, 0, n, n, format="csr"))
+    return DH @ (L @ DH)
+
+
+@nx._dispatchable(edge_attrs="weight")
+def total_spanning_tree_weight(G, weight=None, root=None):
+    """
+    Returns the total weight of all spanning trees of `G`.
+
+    Kirchoff's Tree Matrix Theorem [1]_, [2]_ states that the determinant of any
+    cofactor of the Laplacian matrix of a graph is the number of spanning trees
+    in the graph. For a weighted Laplacian matrix, it is the sum across all
+    spanning trees of the multiplicative weight of each tree. That is, the
+    weight of each tree is the product of its edge weights.
+
+    For unweighted graphs, the total weight equals the number of spanning trees in `G`.
+
+    For directed graphs, the total weight follows by summing over all directed
+    spanning trees in `G` that start in the `root` node [3]_.
+
+    .. deprecated:: 3.3
+
+       ``total_spanning_tree_weight`` is deprecated and will be removed in v3.5.
+       Use ``nx.number_of_spanning_trees(G)`` instead.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    weight : string or None, optional (default=None)
+        The key for the edge attribute holding the edge weight.
+        If None, then each edge has weight 1.
+
+    root : node (only required for directed graphs)
+       A node in the directed graph `G`.
+
+    Returns
+    -------
+    total_weight : float
+        Undirected graphs:
+            The sum of the total multiplicative weights for all spanning trees in `G`.
+        Directed graphs:
+            The sum of the total multiplicative weights for all spanning trees of `G`,
+            rooted at node `root`.
+
+    Raises
+    ------
+    NetworkXPointlessConcept
+        If `G` does not contain any nodes.
+
+    NetworkXError
+        If the graph `G` is not (weakly) connected,
+        or if `G` is directed and the root node is not specified or not in G.
+
+    Examples
+    --------
+    >>> G = nx.complete_graph(5)
+    >>> round(nx.total_spanning_tree_weight(G))
+    125
+
+    >>> G = nx.Graph()
+    >>> G.add_edge(1, 2, weight=2)
+    >>> G.add_edge(1, 3, weight=1)
+    >>> G.add_edge(2, 3, weight=1)
+    >>> round(nx.total_spanning_tree_weight(G, "weight"))
+    5
+
+    Notes
+    -----
+    Self-loops are excluded. Multi-edges are contracted in one edge
+    equal to the sum of the weights.
+
+    References
+    ----------
+    .. [1] Wikipedia
+       "Kirchhoff's theorem."
+       https://en.wikipedia.org/wiki/Kirchhoff%27s_theorem
+    .. [2] Kirchhoff, G. R.
+        Über die Auflösung der Gleichungen, auf welche man
+        bei der Untersuchung der linearen Vertheilung
+        Galvanischer Ströme geführt wird
+        Annalen der Physik und Chemie, vol. 72, pp. 497-508, 1847.
+    .. [3] Margoliash, J.
+        "Matrix-Tree Theorem for Directed Graphs"
+        https://www.math.uchicago.edu/~may/VIGRE/VIGRE2010/REUPapers/Margoliash.pdf
+    """
+    import warnings
+
+    warnings.warn(
+        (
+            "\n\ntotal_spanning_tree_weight is deprecated and will be removed in v3.5.\n"
+            "Use `nx.number_of_spanning_trees(G)` instead."
+        ),
+        category=DeprecationWarning,
+        stacklevel=3,
+    )
+
+    return nx.number_of_spanning_trees(G, weight=weight, root=root)
+
+
+###############################################################################
+# Code based on work from https://github.com/bjedwards
+
+
+@not_implemented_for("undirected")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def directed_laplacian_matrix(
+    G, nodelist=None, weight="weight", walk_type=None, alpha=0.95
+):
+    r"""Returns the directed Laplacian matrix of G.
+
+    The graph directed Laplacian is the matrix
+
+    .. math::
+
+        L = I - \frac{1}{2} \left (\Phi^{1/2} P \Phi^{-1/2} + \Phi^{-1/2} P^T \Phi^{1/2} \right )
+
+    where `I` is the identity matrix, `P` is the transition matrix of the
+    graph, and `\Phi` a matrix with the Perron vector of `P` in the diagonal and
+    zeros elsewhere [1]_.
+
+    Depending on the value of walk_type, `P` can be the transition matrix
+    induced by a random walk, a lazy random walk, or a random walk with
+    teleportation (PageRank).
+
+    Parameters
+    ----------
+    G : DiGraph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    walk_type : string or None, optional (default=None)
+       One of ``"random"``, ``"lazy"``, or ``"pagerank"``. If ``walk_type=None``
+       (the default), then a value is selected according to the properties of `G`:
+       - ``walk_type="random"`` if `G` is strongly connected and aperiodic
+       - ``walk_type="lazy"`` if `G` is strongly connected but not aperiodic
+       - ``walk_type="pagerank"`` for all other cases.
+
+    alpha : real
+       (1 - alpha) is the teleportation probability used with pagerank
+
+    Returns
+    -------
+    L : NumPy matrix
+      Normalized Laplacian of G.
+
+    Notes
+    -----
+    Only implemented for DiGraphs
+
+    The result is always a symmetric matrix.
+
+    This calculation uses the out-degree of the graph `G`. To use the
+    in-degree for calculations instead, use `G.reverse(copy=False)` and
+    take the transpose.
+
+    See Also
+    --------
+    laplacian_matrix
+    normalized_laplacian_matrix
+    directed_combinatorial_laplacian_matrix
+
+    References
+    ----------
+    .. [1] Fan Chung (2005).
+       Laplacians and the Cheeger inequality for directed graphs.
+       Annals of Combinatorics, 9(1), 2005
+    """
+    import numpy as np
+    import scipy as sp
+
+    # NOTE: P has type ndarray if walk_type=="pagerank", else csr_array
+    P = _transition_matrix(
+        G, nodelist=nodelist, weight=weight, walk_type=walk_type, alpha=alpha
+    )
+
+    n, m = P.shape
+
+    evals, evecs = sp.sparse.linalg.eigs(P.T, k=1)
+    v = evecs.flatten().real
+    p = v / v.sum()
+    # p>=0 by Perron-Frobenius Thm. Use abs() to fix roundoff across zero gh-6865
+    sqrtp = np.sqrt(np.abs(p))
+    Q = (
+        # TODO: rm csr_array wrapper when spdiags creates arrays
+        sp.sparse.csr_array(sp.sparse.spdiags(sqrtp, 0, n, n))
+        @ P
+        # TODO: rm csr_array wrapper when spdiags creates arrays
+        @ sp.sparse.csr_array(sp.sparse.spdiags(1.0 / sqrtp, 0, n, n))
+    )
+    # NOTE: This could be sparsified for the non-pagerank cases
+    I = np.identity(len(G))
+
+    return I - (Q + Q.T) / 2.0
+
+
+@not_implemented_for("undirected")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def directed_combinatorial_laplacian_matrix(
+    G, nodelist=None, weight="weight", walk_type=None, alpha=0.95
+):
+    r"""Return the directed combinatorial Laplacian matrix of G.
+
+    The graph directed combinatorial Laplacian is the matrix
+
+    .. math::
+
+        L = \Phi - \frac{1}{2} \left (\Phi P + P^T \Phi \right)
+
+    where `P` is the transition matrix of the graph and `\Phi` a matrix
+    with the Perron vector of `P` in the diagonal and zeros elsewhere [1]_.
+
+    Depending on the value of walk_type, `P` can be the transition matrix
+    induced by a random walk, a lazy random walk, or a random walk with
+    teleportation (PageRank).
+
+    Parameters
+    ----------
+    G : DiGraph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    walk_type : string or None, optional (default=None)
+        One of ``"random"``, ``"lazy"``, or ``"pagerank"``. If ``walk_type=None``
+        (the default), then a value is selected according to the properties of `G`:
+        - ``walk_type="random"`` if `G` is strongly connected and aperiodic
+        - ``walk_type="lazy"`` if `G` is strongly connected but not aperiodic
+        - ``walk_type="pagerank"`` for all other cases.
+
+    alpha : real
+       (1 - alpha) is the teleportation probability used with pagerank
+
+    Returns
+    -------
+    L : NumPy matrix
+      Combinatorial Laplacian of G.
+
+    Notes
+    -----
+    Only implemented for DiGraphs
+
+    The result is always a symmetric matrix.
+
+    This calculation uses the out-degree of the graph `G`. To use the
+    in-degree for calculations instead, use `G.reverse(copy=False)` and
+    take the transpose.
+
+    See Also
+    --------
+    laplacian_matrix
+    normalized_laplacian_matrix
+    directed_laplacian_matrix
+
+    References
+    ----------
+    .. [1] Fan Chung (2005).
+       Laplacians and the Cheeger inequality for directed graphs.
+       Annals of Combinatorics, 9(1), 2005
+    """
+    import scipy as sp
+
+    P = _transition_matrix(
+        G, nodelist=nodelist, weight=weight, walk_type=walk_type, alpha=alpha
+    )
+
+    n, m = P.shape
+
+    evals, evecs = sp.sparse.linalg.eigs(P.T, k=1)
+    v = evecs.flatten().real
+    p = v / v.sum()
+    # NOTE: could be improved by not densifying
+    # TODO: Rm csr_array wrapper when spdiags array creation becomes available
+    Phi = sp.sparse.csr_array(sp.sparse.spdiags(p, 0, n, n)).toarray()
+
+    return Phi - (Phi @ P + P.T @ Phi) / 2.0
+
+
+def _transition_matrix(G, nodelist=None, weight="weight", walk_type=None, alpha=0.95):
+    """Returns the transition matrix of G.
+
+    This is a row stochastic giving the transition probabilities while
+    performing a random walk on the graph. Depending on the value of walk_type,
+    P can be the transition matrix induced by a random walk, a lazy random walk,
+    or a random walk with teleportation (PageRank).
+
+    Parameters
+    ----------
+    G : DiGraph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    walk_type : string or None, optional (default=None)
+       One of ``"random"``, ``"lazy"``, or ``"pagerank"``. If ``walk_type=None``
+       (the default), then a value is selected according to the properties of `G`:
+        - ``walk_type="random"`` if `G` is strongly connected and aperiodic
+        - ``walk_type="lazy"`` if `G` is strongly connected but not aperiodic
+        - ``walk_type="pagerank"`` for all other cases.
+
+    alpha : real
+       (1 - alpha) is the teleportation probability used with pagerank
+
+    Returns
+    -------
+    P : numpy.ndarray
+      transition matrix of G.
+
+    Raises
+    ------
+    NetworkXError
+        If walk_type not specified or alpha not in valid range
+    """
+    import numpy as np
+    import scipy as sp
+
+    if walk_type is None:
+        if nx.is_strongly_connected(G):
+            if nx.is_aperiodic(G):
+                walk_type = "random"
+            else:
+                walk_type = "lazy"
+        else:
+            walk_type = "pagerank"
+
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, dtype=float)
+    n, m = A.shape
+    if walk_type in ["random", "lazy"]:
+        # TODO: Rm csr_array wrapper when spdiags array creation becomes available
+        DI = sp.sparse.csr_array(sp.sparse.spdiags(1.0 / A.sum(axis=1), 0, n, n))
+        if walk_type == "random":
+            P = DI @ A
+        else:
+            # TODO: Rm csr_array wrapper when identity array creation becomes available
+            I = sp.sparse.csr_array(sp.sparse.identity(n))
+            P = (I + DI @ A) / 2.0
+
+    elif walk_type == "pagerank":
+        if not (0 < alpha < 1):
+            raise nx.NetworkXError("alpha must be between 0 and 1")
+        # this is using a dense representation. NOTE: This should be sparsified!
+        A = A.toarray()
+        # add constant to dangling nodes' row
+        A[A.sum(axis=1) == 0, :] = 1 / n
+        # normalize
+        A = A / A.sum(axis=1)[np.newaxis, :].T
+        P = alpha * A + (1 - alpha) / n
+    else:
+        raise nx.NetworkXError("walk_type must be random, lazy, or pagerank")
+
+    return P
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/modularitymatrix.py b/.venv/lib/python3.12/site-packages/networkx/linalg/modularitymatrix.py
new file mode 100644
index 00000000..0287910b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/modularitymatrix.py
@@ -0,0 +1,166 @@
+"""Modularity matrix of graphs."""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["modularity_matrix", "directed_modularity_matrix"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def modularity_matrix(G, nodelist=None, weight=None):
+    r"""Returns the modularity matrix of G.
+
+    The modularity matrix is the matrix B = A - <A>, where A is the adjacency
+    matrix and <A> is the average adjacency matrix, assuming that the graph
+    is described by the configuration model.
+
+    More specifically, the element B_ij of B is defined as
+
+    .. math::
+        A_{ij} - {k_i k_j \over 2 m}
+
+    where k_i is the degree of node i, and where m is the number of edges
+    in the graph. When weight is set to a name of an attribute edge, Aij, k_i,
+    k_j and m are computed using its value.
+
+    Parameters
+    ----------
+    G : Graph
+       A NetworkX graph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default=None)
+       The edge attribute that holds the numerical value used for
+       the edge weight.  If None then all edge weights are 1.
+
+    Returns
+    -------
+    B : Numpy array
+      The modularity matrix of G.
+
+    Examples
+    --------
+    >>> k = [3, 2, 2, 1, 0]
+    >>> G = nx.havel_hakimi_graph(k)
+    >>> B = nx.modularity_matrix(G)
+
+
+    See Also
+    --------
+    to_numpy_array
+    modularity_spectrum
+    adjacency_matrix
+    directed_modularity_matrix
+
+    References
+    ----------
+    .. [1] M. E. J. Newman, "Modularity and community structure in networks",
+           Proc. Natl. Acad. Sci. USA, vol. 103, pp. 8577-8582, 2006.
+    """
+    import numpy as np
+
+    if nodelist is None:
+        nodelist = list(G)
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, format="csr")
+    k = A.sum(axis=1)
+    m = k.sum() * 0.5
+    # Expected adjacency matrix
+    X = np.outer(k, k) / (2 * m)
+
+    return A - X
+
+
+@not_implemented_for("undirected")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def directed_modularity_matrix(G, nodelist=None, weight=None):
+    """Returns the directed modularity matrix of G.
+
+    The modularity matrix is the matrix B = A - <A>, where A is the adjacency
+    matrix and <A> is the expected adjacency matrix, assuming that the graph
+    is described by the configuration model.
+
+    More specifically, the element B_ij of B is defined as
+
+    .. math::
+        B_{ij} = A_{ij} - k_i^{out} k_j^{in} / m
+
+    where :math:`k_i^{in}` is the in degree of node i, and :math:`k_j^{out}` is the out degree
+    of node j, with m the number of edges in the graph. When weight is set
+    to a name of an attribute edge, Aij, k_i, k_j and m are computed using
+    its value.
+
+    Parameters
+    ----------
+    G : DiGraph
+       A NetworkX DiGraph
+
+    nodelist : list, optional
+       The rows and columns are ordered according to the nodes in nodelist.
+       If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight : string or None, optional (default=None)
+       The edge attribute that holds the numerical value used for
+       the edge weight.  If None then all edge weights are 1.
+
+    Returns
+    -------
+    B : Numpy array
+      The modularity matrix of G.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_edges_from(
+    ...     (
+    ...         (1, 2),
+    ...         (1, 3),
+    ...         (3, 1),
+    ...         (3, 2),
+    ...         (3, 5),
+    ...         (4, 5),
+    ...         (4, 6),
+    ...         (5, 4),
+    ...         (5, 6),
+    ...         (6, 4),
+    ...     )
+    ... )
+    >>> B = nx.directed_modularity_matrix(G)
+
+
+    Notes
+    -----
+    NetworkX defines the element A_ij of the adjacency matrix as 1 if there
+    is a link going from node i to node j. Leicht and Newman use the opposite
+    definition. This explains the different expression for B_ij.
+
+    See Also
+    --------
+    to_numpy_array
+    modularity_spectrum
+    adjacency_matrix
+    modularity_matrix
+
+    References
+    ----------
+    .. [1] E. A. Leicht, M. E. J. Newman,
+        "Community structure in directed networks",
+        Phys. Rev Lett., vol. 100, no. 11, p. 118703, 2008.
+    """
+    import numpy as np
+
+    if nodelist is None:
+        nodelist = list(G)
+    A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, format="csr")
+    k_in = A.sum(axis=0)
+    k_out = A.sum(axis=1)
+    m = k_in.sum()
+    # Expected adjacency matrix
+    X = np.outer(k_out, k_in) / m
+
+    return A - X
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/spectrum.py b/.venv/lib/python3.12/site-packages/networkx/linalg/spectrum.py
new file mode 100644
index 00000000..079b1855
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/spectrum.py
@@ -0,0 +1,186 @@
+"""
+Eigenvalue spectrum of graphs.
+"""
+
+import networkx as nx
+
+__all__ = [
+    "laplacian_spectrum",
+    "adjacency_spectrum",
+    "modularity_spectrum",
+    "normalized_laplacian_spectrum",
+    "bethe_hessian_spectrum",
+]
+
+
+@nx._dispatchable(edge_attrs="weight")
+def laplacian_spectrum(G, weight="weight"):
+    """Returns eigenvalues of the Laplacian of G
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    Returns
+    -------
+    evals : NumPy array
+      Eigenvalues
+
+    Notes
+    -----
+    For MultiGraph/MultiDiGraph, the edges weights are summed.
+    See :func:`~networkx.convert_matrix.to_numpy_array` for other options.
+
+    See Also
+    --------
+    laplacian_matrix
+
+    Examples
+    --------
+    The multiplicity of 0 as an eigenvalue of the laplacian matrix is equal
+    to the number of connected components of G.
+
+    >>> G = nx.Graph()  # Create a graph with 5 nodes and 3 connected components
+    >>> G.add_nodes_from(range(5))
+    >>> G.add_edges_from([(0, 2), (3, 4)])
+    >>> nx.laplacian_spectrum(G)
+    array([0., 0., 0., 2., 2.])
+
+    """
+    import scipy as sp
+
+    return sp.linalg.eigvalsh(nx.laplacian_matrix(G, weight=weight).todense())
+
+
+@nx._dispatchable(edge_attrs="weight")
+def normalized_laplacian_spectrum(G, weight="weight"):
+    """Return eigenvalues of the normalized Laplacian of G
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    Returns
+    -------
+    evals : NumPy array
+      Eigenvalues
+
+    Notes
+    -----
+    For MultiGraph/MultiDiGraph, the edges weights are summed.
+    See to_numpy_array for other options.
+
+    See Also
+    --------
+    normalized_laplacian_matrix
+    """
+    import scipy as sp
+
+    return sp.linalg.eigvalsh(
+        nx.normalized_laplacian_matrix(G, weight=weight).todense()
+    )
+
+
+@nx._dispatchable(edge_attrs="weight")
+def adjacency_spectrum(G, weight="weight"):
+    """Returns eigenvalues of the adjacency matrix of G.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    weight : string or None, optional (default='weight')
+       The edge data key used to compute each value in the matrix.
+       If None, then each edge has weight 1.
+
+    Returns
+    -------
+    evals : NumPy array
+      Eigenvalues
+
+    Notes
+    -----
+    For MultiGraph/MultiDiGraph, the edges weights are summed.
+    See to_numpy_array for other options.
+
+    See Also
+    --------
+    adjacency_matrix
+    """
+    import scipy as sp
+
+    return sp.linalg.eigvals(nx.adjacency_matrix(G, weight=weight).todense())
+
+
+@nx._dispatchable
+def modularity_spectrum(G):
+    """Returns eigenvalues of the modularity matrix of G.
+
+    Parameters
+    ----------
+    G : Graph
+       A NetworkX Graph or DiGraph
+
+    Returns
+    -------
+    evals : NumPy array
+      Eigenvalues
+
+    See Also
+    --------
+    modularity_matrix
+
+    References
+    ----------
+    .. [1] M. E. J. Newman, "Modularity and community structure in networks",
+       Proc. Natl. Acad. Sci. USA, vol. 103, pp. 8577-8582, 2006.
+    """
+    import scipy as sp
+
+    if G.is_directed():
+        return sp.linalg.eigvals(nx.directed_modularity_matrix(G))
+    else:
+        return sp.linalg.eigvals(nx.modularity_matrix(G))
+
+
+@nx._dispatchable
+def bethe_hessian_spectrum(G, r=None):
+    """Returns eigenvalues of the Bethe Hessian matrix of G.
+
+    Parameters
+    ----------
+    G : Graph
+       A NetworkX Graph or DiGraph
+
+    r : float
+       Regularizer parameter
+
+    Returns
+    -------
+    evals : NumPy array
+      Eigenvalues
+
+    See Also
+    --------
+    bethe_hessian_matrix
+
+    References
+    ----------
+    .. [1] A. Saade, F. Krzakala and L. Zdeborová
+       "Spectral clustering of graphs with the bethe hessian",
+       Advances in Neural Information Processing Systems. 2014.
+    """
+    import scipy as sp
+
+    return sp.linalg.eigvalsh(nx.bethe_hessian_matrix(G, r).todense())
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/tests/__init__.py b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/__init__.py
new file mode 100644
index 00000000..e69de29b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/__init__.py
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_algebraic_connectivity.py b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_algebraic_connectivity.py
new file mode 100644
index 00000000..089d917a
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_algebraic_connectivity.py
@@ -0,0 +1,402 @@
+from math import sqrt
+
+import pytest
+
+np = pytest.importorskip("numpy")
+
+
+import networkx as nx
+
+methods = ("tracemin_pcg", "tracemin_lu", "lanczos", "lobpcg")
+
+
+def test_algebraic_connectivity_tracemin_chol():
+    """Test that "tracemin_chol" raises an exception."""
+    pytest.importorskip("scipy")
+    G = nx.barbell_graph(5, 4)
+    with pytest.raises(nx.NetworkXError):
+        nx.algebraic_connectivity(G, method="tracemin_chol")
+
+
+def test_fiedler_vector_tracemin_chol():
+    """Test that "tracemin_chol" raises an exception."""
+    pytest.importorskip("scipy")
+    G = nx.barbell_graph(5, 4)
+    with pytest.raises(nx.NetworkXError):
+        nx.fiedler_vector(G, method="tracemin_chol")
+
+
+def test_spectral_ordering_tracemin_chol():
+    """Test that "tracemin_chol" raises an exception."""
+    pytest.importorskip("scipy")
+    G = nx.barbell_graph(5, 4)
+    with pytest.raises(nx.NetworkXError):
+        nx.spectral_ordering(G, method="tracemin_chol")
+
+
+def test_fiedler_vector_tracemin_unknown():
+    """Test that "tracemin_unknown" raises an exception."""
+    pytest.importorskip("scipy")
+    G = nx.barbell_graph(5, 4)
+    L = nx.laplacian_matrix(G)
+    X = np.asarray(np.random.normal(size=(1, L.shape[0]))).T
+    with pytest.raises(nx.NetworkXError, match="Unknown linear system solver"):
+        nx.linalg.algebraicconnectivity._tracemin_fiedler(
+            L, X, normalized=False, tol=1e-8, method="tracemin_unknown"
+        )
+
+
+def test_spectral_bisection():
+    pytest.importorskip("scipy")
+    G = nx.barbell_graph(3, 0)
+    C = nx.spectral_bisection(G)
+    assert C == ({0, 1, 2}, {3, 4, 5})
+
+    mapping = dict(enumerate("badfec"))
+    G = nx.relabel_nodes(G, mapping)
+    C = nx.spectral_bisection(G)
+    assert C == (
+        {mapping[0], mapping[1], mapping[2]},
+        {mapping[3], mapping[4], mapping[5]},
+    )
+
+
+def check_eigenvector(A, l, x):
+    nx = np.linalg.norm(x)
+    # Check zeroness.
+    assert nx != pytest.approx(0, abs=1e-07)
+    y = A @ x
+    ny = np.linalg.norm(y)
+    # Check collinearity.
+    assert x @ y == pytest.approx(nx * ny, abs=1e-7)
+    # Check eigenvalue.
+    assert ny == pytest.approx(l * nx, abs=1e-7)
+
+
+class TestAlgebraicConnectivity:
+    @pytest.mark.parametrize("method", methods)
+    def test_directed(self, method):
+        G = nx.DiGraph()
+        pytest.raises(
+            nx.NetworkXNotImplemented, nx.algebraic_connectivity, G, method=method
+        )
+        pytest.raises(nx.NetworkXNotImplemented, nx.fiedler_vector, G, method=method)
+
+    @pytest.mark.parametrize("method", methods)
+    def test_null_and_singleton(self, method):
+        G = nx.Graph()
+        pytest.raises(nx.NetworkXError, nx.algebraic_connectivity, G, method=method)
+        pytest.raises(nx.NetworkXError, nx.fiedler_vector, G, method=method)
+        G.add_edge(0, 0)
+        pytest.raises(nx.NetworkXError, nx.algebraic_connectivity, G, method=method)
+        pytest.raises(nx.NetworkXError, nx.fiedler_vector, G, method=method)
+
+    @pytest.mark.parametrize("method", methods)
+    def test_disconnected(self, method):
+        G = nx.Graph()
+        G.add_nodes_from(range(2))
+        assert nx.algebraic_connectivity(G) == 0
+        pytest.raises(nx.NetworkXError, nx.fiedler_vector, G, method=method)
+        G.add_edge(0, 1, weight=0)
+        assert nx.algebraic_connectivity(G) == 0
+        pytest.raises(nx.NetworkXError, nx.fiedler_vector, G, method=method)
+
+    def test_unrecognized_method(self):
+        pytest.importorskip("scipy")
+        G = nx.path_graph(4)
+        pytest.raises(nx.NetworkXError, nx.algebraic_connectivity, G, method="unknown")
+        pytest.raises(nx.NetworkXError, nx.fiedler_vector, G, method="unknown")
+
+    @pytest.mark.parametrize("method", methods)
+    def test_two_nodes(self, method):
+        pytest.importorskip("scipy")
+        G = nx.Graph()
+        G.add_edge(0, 1, weight=1)
+        A = nx.laplacian_matrix(G)
+        assert nx.algebraic_connectivity(G, tol=1e-12, method=method) == pytest.approx(
+            2, abs=1e-7
+        )
+        x = nx.fiedler_vector(G, tol=1e-12, method=method)
+        check_eigenvector(A, 2, x)
+
+    @pytest.mark.parametrize("method", methods)
+    def test_two_nodes_multigraph(self, method):
+        pytest.importorskip("scipy")
+        G = nx.MultiGraph()
+        G.add_edge(0, 0, spam=1e8)
+        G.add_edge(0, 1, spam=1)
+        G.add_edge(0, 1, spam=-2)
+        A = -3 * nx.laplacian_matrix(G, weight="spam")
+        assert nx.algebraic_connectivity(
+            G, weight="spam", tol=1e-12, method=method
+        ) == pytest.approx(6, abs=1e-7)
+        x = nx.fiedler_vector(G, weight="spam", tol=1e-12, method=method)
+        check_eigenvector(A, 6, x)
+
+    def test_abbreviation_of_method(self):
+        pytest.importorskip("scipy")
+        G = nx.path_graph(8)
+        A = nx.laplacian_matrix(G)
+        sigma = 2 - sqrt(2 + sqrt(2))
+        ac = nx.algebraic_connectivity(G, tol=1e-12, method="tracemin")
+        assert ac == pytest.approx(sigma, abs=1e-7)
+        x = nx.fiedler_vector(G, tol=1e-12, method="tracemin")
+        check_eigenvector(A, sigma, x)
+
+    @pytest.mark.parametrize("method", methods)
+    def test_path(self, method):
+        pytest.importorskip("scipy")
+        G = nx.path_graph(8)
+        A = nx.laplacian_matrix(G)
+        sigma = 2 - sqrt(2 + sqrt(2))
+        ac = nx.algebraic_connectivity(G, tol=1e-12, method=method)
+        assert ac == pytest.approx(sigma, abs=1e-7)
+        x = nx.fiedler_vector(G, tol=1e-12, method=method)
+        check_eigenvector(A, sigma, x)
+
+    @pytest.mark.parametrize("method", methods)
+    def test_problematic_graph_issue_2381(self, method):
+        pytest.importorskip("scipy")
+        G = nx.path_graph(4)
+        G.add_edges_from([(4, 2), (5, 1)])
+        A = nx.laplacian_matrix(G)
+        sigma = 0.438447187191
+        ac = nx.algebraic_connectivity(G, tol=1e-12, method=method)
+        assert ac == pytest.approx(sigma, abs=1e-7)
+        x = nx.fiedler_vector(G, tol=1e-12, method=method)
+        check_eigenvector(A, sigma, x)
+
+    @pytest.mark.parametrize("method", methods)
+    def test_cycle(self, method):
+        pytest.importorskip("scipy")
+        G = nx.cycle_graph(8)
+        A = nx.laplacian_matrix(G)
+        sigma = 2 - sqrt(2)
+        ac = nx.algebraic_connectivity(G, tol=1e-12, method=method)
+        assert ac == pytest.approx(sigma, abs=1e-7)
+        x = nx.fiedler_vector(G, tol=1e-12, method=method)
+        check_eigenvector(A, sigma, x)
+
+    @pytest.mark.parametrize("method", methods)
+    def test_seed_argument(self, method):
+        pytest.importorskip("scipy")
+        G = nx.cycle_graph(8)
+        A = nx.laplacian_matrix(G)
+        sigma = 2 - sqrt(2)
+        ac = nx.algebraic_connectivity(G, tol=1e-12, method=method, seed=1)
+        assert ac == pytest.approx(sigma, abs=1e-7)
+        x = nx.fiedler_vector(G, tol=1e-12, method=method, seed=1)
+        check_eigenvector(A, sigma, x)
+
+    @pytest.mark.parametrize(
+        ("normalized", "sigma", "laplacian_fn"),
+        (
+            (False, 0.2434017461399311, nx.laplacian_matrix),
+            (True, 0.08113391537997749, nx.normalized_laplacian_matrix),
+        ),
+    )
+    @pytest.mark.parametrize("method", methods)
+    def test_buckminsterfullerene(self, normalized, sigma, laplacian_fn, method):
+        pytest.importorskip("scipy")
+        G = nx.Graph(
+            [
+                (1, 10),
+                (1, 41),
+                (1, 59),
+                (2, 12),
+                (2, 42),
+                (2, 60),
+                (3, 6),
+                (3, 43),
+                (3, 57),
+                (4, 8),
+                (4, 44),
+                (4, 58),
+                (5, 13),
+                (5, 56),
+                (5, 57),
+                (6, 10),
+                (6, 31),
+                (7, 14),
+                (7, 56),
+                (7, 58),
+                (8, 12),
+                (8, 32),
+                (9, 23),
+                (9, 53),
+                (9, 59),
+                (10, 15),
+                (11, 24),
+                (11, 53),
+                (11, 60),
+                (12, 16),
+                (13, 14),
+                (13, 25),
+                (14, 26),
+                (15, 27),
+                (15, 49),
+                (16, 28),
+                (16, 50),
+                (17, 18),
+                (17, 19),
+                (17, 54),
+                (18, 20),
+                (18, 55),
+                (19, 23),
+                (19, 41),
+                (20, 24),
+                (20, 42),
+                (21, 31),
+                (21, 33),
+                (21, 57),
+                (22, 32),
+                (22, 34),
+                (22, 58),
+                (23, 24),
+                (25, 35),
+                (25, 43),
+                (26, 36),
+                (26, 44),
+                (27, 51),
+                (27, 59),
+                (28, 52),
+                (28, 60),
+                (29, 33),
+                (29, 34),
+                (29, 56),
+                (30, 51),
+                (30, 52),
+                (30, 53),
+                (31, 47),
+                (32, 48),
+                (33, 45),
+                (34, 46),
+                (35, 36),
+                (35, 37),
+                (36, 38),
+                (37, 39),
+                (37, 49),
+                (38, 40),
+                (38, 50),
+                (39, 40),
+                (39, 51),
+                (40, 52),
+                (41, 47),
+                (42, 48),
+                (43, 49),
+                (44, 50),
+                (45, 46),
+                (45, 54),
+                (46, 55),
+                (47, 54),
+                (48, 55),
+            ]
+        )
+        A = laplacian_fn(G)
+        try:
+            assert nx.algebraic_connectivity(
+                G, normalized=normalized, tol=1e-12, method=method
+            ) == pytest.approx(sigma, abs=1e-7)
+            x = nx.fiedler_vector(G, normalized=normalized, tol=1e-12, method=method)
+            check_eigenvector(A, sigma, x)
+        except nx.NetworkXError as err:
+            if err.args not in (
+                ("Cholesky solver unavailable.",),
+                ("LU solver unavailable.",),
+            ):
+                raise
+
+
+class TestSpectralOrdering:
+    _graphs = (nx.Graph, nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)
+
+    @pytest.mark.parametrize("graph", _graphs)
+    def test_nullgraph(self, graph):
+        G = graph()
+        pytest.raises(nx.NetworkXError, nx.spectral_ordering, G)
+
+    @pytest.mark.parametrize("graph", _graphs)
+    def test_singleton(self, graph):
+        G = graph()
+        G.add_node("x")
+        assert nx.spectral_ordering(G) == ["x"]
+        G.add_edge("x", "x", weight=33)
+        G.add_edge("x", "x", weight=33)
+        assert nx.spectral_ordering(G) == ["x"]
+
+    def test_unrecognized_method(self):
+        G = nx.path_graph(4)
+        pytest.raises(nx.NetworkXError, nx.spectral_ordering, G, method="unknown")
+
+    @pytest.mark.parametrize("method", methods)
+    def test_three_nodes(self, method):
+        pytest.importorskip("scipy")
+        G = nx.Graph()
+        G.add_weighted_edges_from([(1, 2, 1), (1, 3, 2), (2, 3, 1)], weight="spam")
+        order = nx.spectral_ordering(G, weight="spam", method=method)
+        assert set(order) == set(G)
+        assert {1, 3} in (set(order[:-1]), set(order[1:]))
+
+    @pytest.mark.parametrize("method", methods)
+    def test_three_nodes_multigraph(self, method):
+        pytest.importorskip("scipy")
+        G = nx.MultiDiGraph()
+        G.add_weighted_edges_from([(1, 2, 1), (1, 3, 2), (2, 3, 1), (2, 3, 2)])
+        order = nx.spectral_ordering(G, method=method)
+        assert set(order) == set(G)
+        assert {2, 3} in (set(order[:-1]), set(order[1:]))
+
+    @pytest.mark.parametrize("method", methods)
+    def test_path(self, method):
+        pytest.importorskip("scipy")
+        path = list(range(10))
+        np.random.shuffle(path)
+        G = nx.Graph()
+        nx.add_path(G, path)
+        order = nx.spectral_ordering(G, method=method)
+        assert order in [path, list(reversed(path))]
+
+    @pytest.mark.parametrize("method", methods)
+    def test_seed_argument(self, method):
+        pytest.importorskip("scipy")
+        path = list(range(10))
+        np.random.shuffle(path)
+        G = nx.Graph()
+        nx.add_path(G, path)
+        order = nx.spectral_ordering(G, method=method, seed=1)
+        assert order in [path, list(reversed(path))]
+
+    @pytest.mark.parametrize("method", methods)
+    def test_disconnected(self, method):
+        pytest.importorskip("scipy")
+        G = nx.Graph()
+        nx.add_path(G, range(0, 10, 2))
+        nx.add_path(G, range(1, 10, 2))
+        order = nx.spectral_ordering(G, method=method)
+        assert set(order) == set(G)
+        seqs = [
+            list(range(0, 10, 2)),
+            list(range(8, -1, -2)),
+            list(range(1, 10, 2)),
+            list(range(9, -1, -2)),
+        ]
+        assert order[:5] in seqs
+        assert order[5:] in seqs
+
+    @pytest.mark.parametrize(
+        ("normalized", "expected_order"),
+        (
+            (False, [[1, 2, 0, 3, 4, 5, 6, 9, 7, 8], [8, 7, 9, 6, 5, 4, 3, 0, 2, 1]]),
+            (True, [[1, 2, 3, 0, 4, 5, 9, 6, 7, 8], [8, 7, 6, 9, 5, 4, 0, 3, 2, 1]]),
+        ),
+    )
+    @pytest.mark.parametrize("method", methods)
+    def test_cycle(self, normalized, expected_order, method):
+        pytest.importorskip("scipy")
+        path = list(range(10))
+        G = nx.Graph()
+        nx.add_path(G, path, weight=5)
+        G.add_edge(path[-1], path[0], weight=1)
+        A = nx.laplacian_matrix(G).todense()
+        order = nx.spectral_ordering(G, normalized=normalized, method=method)
+        assert order in expected_order
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_attrmatrix.py b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_attrmatrix.py
new file mode 100644
index 00000000..01574bb3
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_attrmatrix.py
@@ -0,0 +1,108 @@
+import pytest
+
+np = pytest.importorskip("numpy")
+
+import networkx as nx
+
+
+def test_attr_matrix():
+    G = nx.Graph()
+    G.add_edge(0, 1, thickness=1, weight=3)
+    G.add_edge(0, 1, thickness=1, weight=3)
+    G.add_edge(0, 2, thickness=2)
+    G.add_edge(1, 2, thickness=3)
+
+    def node_attr(u):
+        return G.nodes[u].get("size", 0.5) * 3
+
+    def edge_attr(u, v):
+        return G[u][v].get("thickness", 0.5)
+
+    M = nx.attr_matrix(G, edge_attr=edge_attr, node_attr=node_attr)
+    np.testing.assert_equal(M[0], np.array([[6.0]]))
+    assert M[1] == [1.5]
+
+
+def test_attr_matrix_directed():
+    G = nx.DiGraph()
+    G.add_edge(0, 1, thickness=1, weight=3)
+    G.add_edge(0, 1, thickness=1, weight=3)
+    G.add_edge(0, 2, thickness=2)
+    G.add_edge(1, 2, thickness=3)
+    M = nx.attr_matrix(G, rc_order=[0, 1, 2])
+    # fmt: off
+    data = np.array(
+        [[0., 1., 1.],
+         [0., 0., 1.],
+         [0., 0., 0.]]
+    )
+    # fmt: on
+    np.testing.assert_equal(M, np.array(data))
+
+
+def test_attr_matrix_multigraph():
+    G = nx.MultiGraph()
+    G.add_edge(0, 1, thickness=1, weight=3)
+    G.add_edge(0, 1, thickness=1, weight=3)
+    G.add_edge(0, 1, thickness=1, weight=3)
+    G.add_edge(0, 2, thickness=2)
+    G.add_edge(1, 2, thickness=3)
+    M = nx.attr_matrix(G, rc_order=[0, 1, 2])
+    # fmt: off
+    data = np.array(
+        [[0., 3., 1.],
+         [3., 0., 1.],
+         [1., 1., 0.]]
+    )
+    # fmt: on
+    np.testing.assert_equal(M, np.array(data))
+    M = nx.attr_matrix(G, edge_attr="weight", rc_order=[0, 1, 2])
+    # fmt: off
+    data = np.array(
+        [[0., 9., 1.],
+         [9., 0., 1.],
+         [1., 1., 0.]]
+    )
+    # fmt: on
+    np.testing.assert_equal(M, np.array(data))
+    M = nx.attr_matrix(G, edge_attr="thickness", rc_order=[0, 1, 2])
+    # fmt: off
+    data = np.array(
+        [[0., 3., 2.],
+         [3., 0., 3.],
+         [2., 3., 0.]]
+    )
+    # fmt: on
+    np.testing.assert_equal(M, np.array(data))
+
+
+def test_attr_sparse_matrix():
+    pytest.importorskip("scipy")
+    G = nx.Graph()
+    G.add_edge(0, 1, thickness=1, weight=3)
+    G.add_edge(0, 2, thickness=2)
+    G.add_edge(1, 2, thickness=3)
+    M = nx.attr_sparse_matrix(G)
+    mtx = M[0]
+    data = np.ones((3, 3), float)
+    np.fill_diagonal(data, 0)
+    np.testing.assert_equal(mtx.todense(), np.array(data))
+    assert M[1] == [0, 1, 2]
+
+
+def test_attr_sparse_matrix_directed():
+    pytest.importorskip("scipy")
+    G = nx.DiGraph()
+    G.add_edge(0, 1, thickness=1, weight=3)
+    G.add_edge(0, 1, thickness=1, weight=3)
+    G.add_edge(0, 2, thickness=2)
+    G.add_edge(1, 2, thickness=3)
+    M = nx.attr_sparse_matrix(G, rc_order=[0, 1, 2])
+    # fmt: off
+    data = np.array(
+        [[0., 1., 1.],
+         [0., 0., 1.],
+         [0., 0., 0.]]
+    )
+    # fmt: on
+    np.testing.assert_equal(M.todense(), np.array(data))
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_bethehessian.py b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_bethehessian.py
new file mode 100644
index 00000000..339fe1be
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_bethehessian.py
@@ -0,0 +1,41 @@
+import pytest
+
+np = pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+import networkx as nx
+from networkx.generators.degree_seq import havel_hakimi_graph
+
+
+class TestBetheHessian:
+    @classmethod
+    def setup_class(cls):
+        deg = [3, 2, 2, 1, 0]
+        cls.G = havel_hakimi_graph(deg)
+        cls.P = nx.path_graph(3)
+
+    def test_bethe_hessian(self):
+        "Bethe Hessian matrix"
+        # fmt: off
+        H = np.array([[4, -2, 0],
+                      [-2, 5, -2],
+                      [0, -2, 4]])
+        # fmt: on
+        permutation = [2, 0, 1]
+        # Bethe Hessian gives expected form
+        np.testing.assert_equal(nx.bethe_hessian_matrix(self.P, r=2).todense(), H)
+        # nodelist is correctly implemented
+        np.testing.assert_equal(
+            nx.bethe_hessian_matrix(self.P, r=2, nodelist=permutation).todense(),
+            H[np.ix_(permutation, permutation)],
+        )
+        # Equal to Laplacian matrix when r=1
+        np.testing.assert_equal(
+            nx.bethe_hessian_matrix(self.G, r=1).todense(),
+            nx.laplacian_matrix(self.G).todense(),
+        )
+        # Correct default for the regularizer r
+        np.testing.assert_equal(
+            nx.bethe_hessian_matrix(self.G).todense(),
+            nx.bethe_hessian_matrix(self.G, r=1.25).todense(),
+        )
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_graphmatrix.py b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_graphmatrix.py
new file mode 100644
index 00000000..519198bc
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_graphmatrix.py
@@ -0,0 +1,276 @@
+import pytest
+
+np = pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+import networkx as nx
+from networkx.exception import NetworkXError
+from networkx.generators.degree_seq import havel_hakimi_graph
+
+
+def test_incidence_matrix_simple():
+    deg = [3, 2, 2, 1, 0]
+    G = havel_hakimi_graph(deg)
+    deg = [(1, 0), (1, 0), (1, 0), (2, 0), (1, 0), (2, 1), (0, 1), (0, 1)]
+    MG = nx.random_clustered_graph(deg, seed=42)
+
+    I = nx.incidence_matrix(G, dtype=int).todense()
+    # fmt: off
+    expected = np.array(
+        [[1, 1, 1, 0],
+         [0, 1, 0, 1],
+         [1, 0, 0, 1],
+         [0, 0, 1, 0],
+         [0, 0, 0, 0]]
+    )
+    # fmt: on
+    np.testing.assert_equal(I, expected)
+
+    I = nx.incidence_matrix(MG, dtype=int).todense()
+    # fmt: off
+    expected = np.array(
+        [[1, 0, 0, 0, 0, 0, 0],
+         [1, 0, 0, 0, 0, 0, 0],
+         [0, 1, 0, 0, 0, 0, 0],
+         [0, 0, 0, 0, 0, 0, 0],
+         [0, 1, 0, 0, 0, 0, 0],
+         [0, 0, 0, 0, 1, 1, 0],
+         [0, 0, 0, 0, 0, 1, 1],
+         [0, 0, 0, 0, 1, 0, 1]]
+    )
+    # fmt: on
+    np.testing.assert_equal(I, expected)
+
+    with pytest.raises(NetworkXError):
+        nx.incidence_matrix(G, nodelist=[0, 1])
+
+
+class TestGraphMatrix:
+    @classmethod
+    def setup_class(cls):
+        deg = [3, 2, 2, 1, 0]
+        cls.G = havel_hakimi_graph(deg)
+        # fmt: off
+        cls.OI = np.array(
+            [[-1, -1, -1, 0],
+             [1, 0, 0, -1],
+             [0, 1, 0, 1],
+             [0, 0, 1, 0],
+             [0, 0, 0, 0]]
+        )
+        cls.A = np.array(
+            [[0, 1, 1, 1, 0],
+             [1, 0, 1, 0, 0],
+             [1, 1, 0, 0, 0],
+             [1, 0, 0, 0, 0],
+             [0, 0, 0, 0, 0]]
+        )
+        # fmt: on
+        cls.WG = havel_hakimi_graph(deg)
+        cls.WG.add_edges_from(
+            (u, v, {"weight": 0.5, "other": 0.3}) for (u, v) in cls.G.edges()
+        )
+        # fmt: off
+        cls.WA = np.array(
+            [[0, 0.5, 0.5, 0.5, 0],
+             [0.5, 0, 0.5, 0, 0],
+             [0.5, 0.5, 0, 0, 0],
+             [0.5, 0, 0, 0, 0],
+             [0, 0, 0, 0, 0]]
+        )
+        # fmt: on
+        cls.MG = nx.MultiGraph(cls.G)
+        cls.MG2 = cls.MG.copy()
+        cls.MG2.add_edge(0, 1)
+        # fmt: off
+        cls.MG2A = np.array(
+            [[0, 2, 1, 1, 0],
+             [2, 0, 1, 0, 0],
+             [1, 1, 0, 0, 0],
+             [1, 0, 0, 0, 0],
+             [0, 0, 0, 0, 0]]
+        )
+        cls.MGOI = np.array(
+            [[-1, -1, -1, -1, 0],
+             [1, 1, 0, 0, -1],
+             [0, 0, 1, 0, 1],
+             [0, 0, 0, 1, 0],
+             [0, 0, 0, 0, 0]]
+        )
+        # fmt: on
+        cls.no_edges_G = nx.Graph([(1, 2), (3, 2, {"weight": 8})])
+        cls.no_edges_A = np.array([[0, 0], [0, 0]])
+
+    def test_incidence_matrix(self):
+        "Conversion to incidence matrix"
+        I = nx.incidence_matrix(
+            self.G,
+            nodelist=sorted(self.G),
+            edgelist=sorted(self.G.edges()),
+            oriented=True,
+            dtype=int,
+        ).todense()
+        np.testing.assert_equal(I, self.OI)
+
+        I = nx.incidence_matrix(
+            self.G,
+            nodelist=sorted(self.G),
+            edgelist=sorted(self.G.edges()),
+            oriented=False,
+            dtype=int,
+        ).todense()
+        np.testing.assert_equal(I, np.abs(self.OI))
+
+        I = nx.incidence_matrix(
+            self.MG,
+            nodelist=sorted(self.MG),
+            edgelist=sorted(self.MG.edges()),
+            oriented=True,
+            dtype=int,
+        ).todense()
+        np.testing.assert_equal(I, self.OI)
+
+        I = nx.incidence_matrix(
+            self.MG,
+            nodelist=sorted(self.MG),
+            edgelist=sorted(self.MG.edges()),
+            oriented=False,
+            dtype=int,
+        ).todense()
+        np.testing.assert_equal(I, np.abs(self.OI))
+
+        I = nx.incidence_matrix(
+            self.MG2,
+            nodelist=sorted(self.MG2),
+            edgelist=sorted(self.MG2.edges()),
+            oriented=True,
+            dtype=int,
+        ).todense()
+        np.testing.assert_equal(I, self.MGOI)
+
+        I = nx.incidence_matrix(
+            self.MG2,
+            nodelist=sorted(self.MG),
+            edgelist=sorted(self.MG2.edges()),
+            oriented=False,
+            dtype=int,
+        ).todense()
+        np.testing.assert_equal(I, np.abs(self.MGOI))
+
+        I = nx.incidence_matrix(self.G, dtype=np.uint8)
+        assert I.dtype == np.uint8
+
+    def test_weighted_incidence_matrix(self):
+        I = nx.incidence_matrix(
+            self.WG,
+            nodelist=sorted(self.WG),
+            edgelist=sorted(self.WG.edges()),
+            oriented=True,
+            dtype=int,
+        ).todense()
+        np.testing.assert_equal(I, self.OI)
+
+        I = nx.incidence_matrix(
+            self.WG,
+            nodelist=sorted(self.WG),
+            edgelist=sorted(self.WG.edges()),
+            oriented=False,
+            dtype=int,
+        ).todense()
+        np.testing.assert_equal(I, np.abs(self.OI))
+
+        # np.testing.assert_equal(nx.incidence_matrix(self.WG,oriented=True,
+        #                                  weight='weight').todense(),0.5*self.OI)
+        # np.testing.assert_equal(nx.incidence_matrix(self.WG,weight='weight').todense(),
+        #              np.abs(0.5*self.OI))
+        # np.testing.assert_equal(nx.incidence_matrix(self.WG,oriented=True,weight='other').todense(),
+        #              0.3*self.OI)
+
+        I = nx.incidence_matrix(
+            self.WG,
+            nodelist=sorted(self.WG),
+            edgelist=sorted(self.WG.edges()),
+            oriented=True,
+            weight="weight",
+        ).todense()
+        np.testing.assert_equal(I, 0.5 * self.OI)
+
+        I = nx.incidence_matrix(
+            self.WG,
+            nodelist=sorted(self.WG),
+            edgelist=sorted(self.WG.edges()),
+            oriented=False,
+            weight="weight",
+        ).todense()
+        np.testing.assert_equal(I, np.abs(0.5 * self.OI))
+
+        I = nx.incidence_matrix(
+            self.WG,
+            nodelist=sorted(self.WG),
+            edgelist=sorted(self.WG.edges()),
+            oriented=True,
+            weight="other",
+        ).todense()
+        np.testing.assert_equal(I, 0.3 * self.OI)
+
+        # WMG=nx.MultiGraph(self.WG)
+        # WMG.add_edge(0,1,weight=0.5,other=0.3)
+        # np.testing.assert_equal(nx.incidence_matrix(WMG,weight='weight').todense(),
+        #              np.abs(0.5*self.MGOI))
+        # np.testing.assert_equal(nx.incidence_matrix(WMG,weight='weight',oriented=True).todense(),
+        #              0.5*self.MGOI)
+        # np.testing.assert_equal(nx.incidence_matrix(WMG,weight='other',oriented=True).todense(),
+        #              0.3*self.MGOI)
+
+        WMG = nx.MultiGraph(self.WG)
+        WMG.add_edge(0, 1, weight=0.5, other=0.3)
+
+        I = nx.incidence_matrix(
+            WMG,
+            nodelist=sorted(WMG),
+            edgelist=sorted(WMG.edges(keys=True)),
+            oriented=True,
+            weight="weight",
+        ).todense()
+        np.testing.assert_equal(I, 0.5 * self.MGOI)
+
+        I = nx.incidence_matrix(
+            WMG,
+            nodelist=sorted(WMG),
+            edgelist=sorted(WMG.edges(keys=True)),
+            oriented=False,
+            weight="weight",
+        ).todense()
+        np.testing.assert_equal(I, np.abs(0.5 * self.MGOI))
+
+        I = nx.incidence_matrix(
+            WMG,
+            nodelist=sorted(WMG),
+            edgelist=sorted(WMG.edges(keys=True)),
+            oriented=True,
+            weight="other",
+        ).todense()
+        np.testing.assert_equal(I, 0.3 * self.MGOI)
+
+    def test_adjacency_matrix(self):
+        "Conversion to adjacency matrix"
+        np.testing.assert_equal(nx.adjacency_matrix(self.G).todense(), self.A)
+        np.testing.assert_equal(nx.adjacency_matrix(self.MG).todense(), self.A)
+        np.testing.assert_equal(nx.adjacency_matrix(self.MG2).todense(), self.MG2A)
+        np.testing.assert_equal(
+            nx.adjacency_matrix(self.G, nodelist=[0, 1]).todense(), self.A[:2, :2]
+        )
+        np.testing.assert_equal(nx.adjacency_matrix(self.WG).todense(), self.WA)
+        np.testing.assert_equal(
+            nx.adjacency_matrix(self.WG, weight=None).todense(), self.A
+        )
+        np.testing.assert_equal(
+            nx.adjacency_matrix(self.MG2, weight=None).todense(), self.MG2A
+        )
+        np.testing.assert_equal(
+            nx.adjacency_matrix(self.WG, weight="other").todense(), 0.6 * self.WA
+        )
+        np.testing.assert_equal(
+            nx.adjacency_matrix(self.no_edges_G, nodelist=[1, 3]).todense(),
+            self.no_edges_A,
+        )
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_laplacian.py b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_laplacian.py
new file mode 100644
index 00000000..23f1b28e
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_laplacian.py
@@ -0,0 +1,336 @@
+import pytest
+
+np = pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+import networkx as nx
+from networkx.generators.degree_seq import havel_hakimi_graph
+from networkx.generators.expanders import margulis_gabber_galil_graph
+
+
+class TestLaplacian:
+    @classmethod
+    def setup_class(cls):
+        deg = [3, 2, 2, 1, 0]
+        cls.G = havel_hakimi_graph(deg)
+        cls.WG = nx.Graph(
+            (u, v, {"weight": 0.5, "other": 0.3}) for (u, v) in cls.G.edges()
+        )
+        cls.WG.add_node(4)
+        cls.MG = nx.MultiGraph(cls.G)
+
+        # Graph with clsloops
+        cls.Gsl = cls.G.copy()
+        for node in cls.Gsl.nodes():
+            cls.Gsl.add_edge(node, node)
+
+        # Graph used as an example in Sec. 4.1 of Langville and Meyer,
+        # "Google's PageRank and Beyond".
+        cls.DiG = nx.DiGraph()
+        cls.DiG.add_edges_from(
+            (
+                (1, 2),
+                (1, 3),
+                (3, 1),
+                (3, 2),
+                (3, 5),
+                (4, 5),
+                (4, 6),
+                (5, 4),
+                (5, 6),
+                (6, 4),
+            )
+        )
+        cls.DiMG = nx.MultiDiGraph(cls.DiG)
+        cls.DiWG = nx.DiGraph(
+            (u, v, {"weight": 0.5, "other": 0.3}) for (u, v) in cls.DiG.edges()
+        )
+        cls.DiGsl = cls.DiG.copy()
+        for node in cls.DiGsl.nodes():
+            cls.DiGsl.add_edge(node, node)
+
+    def test_laplacian(self):
+        "Graph Laplacian"
+        # fmt: off
+        NL = np.array([[ 3, -1, -1, -1,  0],
+                       [-1,  2, -1,  0,  0],
+                       [-1, -1,  2,  0,  0],
+                       [-1,  0,  0,  1,  0],
+                       [ 0,  0,  0,  0,  0]])
+        # fmt: on
+        WL = 0.5 * NL
+        OL = 0.3 * NL
+        # fmt: off
+        DiNL = np.array([[ 2, -1, -1,  0,  0,  0],
+                         [ 0,  0,  0,  0,  0,  0],
+                         [-1, -1,  3, -1,  0,  0],
+                         [ 0,  0,  0,  2, -1, -1],
+                         [ 0,  0,  0, -1,  2, -1],
+                         [ 0,  0,  0,  0, -1,  1]])
+        # fmt: on
+        DiWL = 0.5 * DiNL
+        DiOL = 0.3 * DiNL
+        np.testing.assert_equal(nx.laplacian_matrix(self.G).todense(), NL)
+        np.testing.assert_equal(nx.laplacian_matrix(self.MG).todense(), NL)
+        np.testing.assert_equal(
+            nx.laplacian_matrix(self.G, nodelist=[0, 1]).todense(),
+            np.array([[1, -1], [-1, 1]]),
+        )
+        np.testing.assert_equal(nx.laplacian_matrix(self.WG).todense(), WL)
+        np.testing.assert_equal(nx.laplacian_matrix(self.WG, weight=None).todense(), NL)
+        np.testing.assert_equal(
+            nx.laplacian_matrix(self.WG, weight="other").todense(), OL
+        )
+
+        np.testing.assert_equal(nx.laplacian_matrix(self.DiG).todense(), DiNL)
+        np.testing.assert_equal(nx.laplacian_matrix(self.DiMG).todense(), DiNL)
+        np.testing.assert_equal(
+            nx.laplacian_matrix(self.DiG, nodelist=[1, 2]).todense(),
+            np.array([[1, -1], [0, 0]]),
+        )
+        np.testing.assert_equal(nx.laplacian_matrix(self.DiWG).todense(), DiWL)
+        np.testing.assert_equal(
+            nx.laplacian_matrix(self.DiWG, weight=None).todense(), DiNL
+        )
+        np.testing.assert_equal(
+            nx.laplacian_matrix(self.DiWG, weight="other").todense(), DiOL
+        )
+
+    def test_normalized_laplacian(self):
+        "Generalized Graph Laplacian"
+        # fmt: off
+        G = np.array([[ 1.   , -0.408, -0.408, -0.577,  0.],
+                      [-0.408,  1.   , -0.5  ,  0.   ,  0.],
+                      [-0.408, -0.5  ,  1.   ,  0.   ,  0.],
+                      [-0.577,  0.   ,  0.   ,  1.   ,  0.],
+                      [ 0.   ,  0.   ,  0.   ,  0.   ,  0.]])
+        GL = np.array([[ 1.   , -0.408, -0.408, -0.577,  0.   ],
+                       [-0.408,  1.   , -0.5  ,  0.   ,  0.   ],
+                       [-0.408, -0.5  ,  1.   ,  0.   ,  0.   ],
+                       [-0.577,  0.   ,  0.   ,  1.   ,  0.   ],
+                       [ 0.   ,  0.   ,  0.   ,  0.   ,  0.   ]])
+        Lsl = np.array([[ 0.75  , -0.2887, -0.2887, -0.3536,  0.    ],
+                        [-0.2887,  0.6667, -0.3333,  0.    ,  0.    ],
+                        [-0.2887, -0.3333,  0.6667,  0.    ,  0.    ],
+                        [-0.3536,  0.    ,  0.    ,  0.5   ,  0.    ],
+                        [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ]])
+
+        DiG = np.array([[ 1.    ,  0.    , -0.4082,  0.    ,  0.    ,  0.    ],
+                        [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
+                        [-0.4082,  0.    ,  1.    ,  0.    , -0.4082,  0.    ],
+                        [ 0.    ,  0.    ,  0.    ,  1.    , -0.5   , -0.7071],
+                        [ 0.    ,  0.    ,  0.    , -0.5   ,  1.    , -0.7071],
+                        [ 0.    ,  0.    ,  0.    , -0.7071,  0.     , 1.    ]])
+        DiGL = np.array([[ 1.    ,  0.    , -0.4082,  0.    ,  0.    ,  0.    ],
+                         [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
+                         [-0.4082,  0.    ,  1.    , -0.4082,  0.    ,  0.    ],
+                         [ 0.    ,  0.    ,  0.    ,  1.    , -0.5   , -0.7071],
+                         [ 0.    ,  0.    ,  0.    , -0.5   ,  1.    , -0.7071],
+                         [ 0.    ,  0.    ,  0.    ,  0.    , -0.7071,  1.    ]])
+        DiLsl = np.array([[ 0.6667, -0.5774, -0.2887,  0.    ,  0.    ,  0.    ],
+                          [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],
+                          [-0.2887, -0.5   ,  0.75  , -0.2887,  0.    ,  0.    ],
+                          [ 0.    ,  0.    ,  0.    ,  0.6667, -0.3333, -0.4082],
+                          [ 0.    ,  0.    ,  0.    , -0.3333,  0.6667, -0.4082],
+                          [ 0.    ,  0.    ,  0.    ,  0.    , -0.4082,  0.5   ]])
+        # fmt: on
+
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(self.G, nodelist=range(5)).todense(),
+            G,
+            decimal=3,
+        )
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(self.G).todense(), GL, decimal=3
+        )
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(self.MG).todense(), GL, decimal=3
+        )
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(self.WG).todense(), GL, decimal=3
+        )
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(self.WG, weight="other").todense(),
+            GL,
+            decimal=3,
+        )
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(self.Gsl).todense(), Lsl, decimal=3
+        )
+
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(
+                self.DiG,
+                nodelist=range(1, 1 + 6),
+            ).todense(),
+            DiG,
+            decimal=3,
+        )
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(self.DiG).todense(), DiGL, decimal=3
+        )
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(self.DiMG).todense(), DiGL, decimal=3
+        )
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(self.DiWG).todense(), DiGL, decimal=3
+        )
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(self.DiWG, weight="other").todense(),
+            DiGL,
+            decimal=3,
+        )
+        np.testing.assert_almost_equal(
+            nx.normalized_laplacian_matrix(self.DiGsl).todense(), DiLsl, decimal=3
+        )
+
+
+def test_directed_laplacian():
+    "Directed Laplacian"
+    # Graph used as an example in Sec. 4.1 of Langville and Meyer,
+    # "Google's PageRank and Beyond". The graph contains dangling nodes, so
+    # the pagerank random walk is selected by directed_laplacian
+    G = nx.DiGraph()
+    G.add_edges_from(
+        (
+            (1, 2),
+            (1, 3),
+            (3, 1),
+            (3, 2),
+            (3, 5),
+            (4, 5),
+            (4, 6),
+            (5, 4),
+            (5, 6),
+            (6, 4),
+        )
+    )
+    # fmt: off
+    GL = np.array([[ 0.9833, -0.2941, -0.3882, -0.0291, -0.0231, -0.0261],
+                   [-0.2941,  0.8333, -0.2339, -0.0536, -0.0589, -0.0554],
+                   [-0.3882, -0.2339,  0.9833, -0.0278, -0.0896, -0.0251],
+                   [-0.0291, -0.0536, -0.0278,  0.9833, -0.4878, -0.6675],
+                   [-0.0231, -0.0589, -0.0896, -0.4878,  0.9833, -0.2078],
+                   [-0.0261, -0.0554, -0.0251, -0.6675, -0.2078,  0.9833]])
+    # fmt: on
+    L = nx.directed_laplacian_matrix(G, alpha=0.9, nodelist=sorted(G))
+    np.testing.assert_almost_equal(L, GL, decimal=3)
+
+    # Make the graph strongly connected, so we can use a random and lazy walk
+    G.add_edges_from(((2, 5), (6, 1)))
+    # fmt: off
+    GL = np.array([[ 1.    , -0.3062, -0.4714,  0.    ,  0.    , -0.3227],
+                   [-0.3062,  1.    , -0.1443,  0.    , -0.3162,  0.    ],
+                   [-0.4714, -0.1443,  1.    ,  0.    , -0.0913,  0.    ],
+                   [ 0.    ,  0.    ,  0.    ,  1.    , -0.5   , -0.5   ],
+                   [ 0.    , -0.3162, -0.0913, -0.5   ,  1.    , -0.25  ],
+                   [-0.3227,  0.    ,  0.    , -0.5   , -0.25  ,  1.    ]])
+    # fmt: on
+    L = nx.directed_laplacian_matrix(
+        G, alpha=0.9, nodelist=sorted(G), walk_type="random"
+    )
+    np.testing.assert_almost_equal(L, GL, decimal=3)
+
+    # fmt: off
+    GL = np.array([[ 0.5   , -0.1531, -0.2357,  0.    ,  0.    , -0.1614],
+                   [-0.1531,  0.5   , -0.0722,  0.    , -0.1581,  0.    ],
+                   [-0.2357, -0.0722,  0.5   ,  0.    , -0.0456,  0.    ],
+                   [ 0.    ,  0.    ,  0.    ,  0.5   , -0.25  , -0.25  ],
+                   [ 0.    , -0.1581, -0.0456, -0.25  ,  0.5   , -0.125 ],
+                   [-0.1614,  0.    ,  0.    , -0.25  , -0.125 ,  0.5   ]])  
+    # fmt: on
+    L = nx.directed_laplacian_matrix(G, alpha=0.9, nodelist=sorted(G), walk_type="lazy")
+    np.testing.assert_almost_equal(L, GL, decimal=3)
+
+    # Make a strongly connected periodic graph
+    G = nx.DiGraph()
+    G.add_edges_from(((1, 2), (2, 4), (4, 1), (1, 3), (3, 4)))
+    # fmt: off
+    GL = np.array([[ 0.5  , -0.176, -0.176, -0.25 ],
+                   [-0.176,  0.5  ,  0.   , -0.176],
+                   [-0.176,  0.   ,  0.5  , -0.176],
+                   [-0.25 , -0.176, -0.176,  0.5  ]])
+    # fmt: on
+    L = nx.directed_laplacian_matrix(G, alpha=0.9, nodelist=sorted(G))
+    np.testing.assert_almost_equal(L, GL, decimal=3)
+
+
+def test_directed_combinatorial_laplacian():
+    "Directed combinatorial Laplacian"
+    # Graph used as an example in Sec. 4.1 of Langville and Meyer,
+    # "Google's PageRank and Beyond". The graph contains dangling nodes, so
+    # the pagerank random walk is selected by directed_laplacian
+    G = nx.DiGraph()
+    G.add_edges_from(
+        (
+            (1, 2),
+            (1, 3),
+            (3, 1),
+            (3, 2),
+            (3, 5),
+            (4, 5),
+            (4, 6),
+            (5, 4),
+            (5, 6),
+            (6, 4),
+        )
+    )
+    # fmt: off
+    GL = np.array([[ 0.0366, -0.0132, -0.0153, -0.0034, -0.0020, -0.0027],
+                   [-0.0132,  0.0450, -0.0111, -0.0076, -0.0062, -0.0069],
+                   [-0.0153, -0.0111,  0.0408, -0.0035, -0.0083, -0.0027],
+                   [-0.0034, -0.0076, -0.0035,  0.3688, -0.1356, -0.2187],
+                   [-0.0020, -0.0062, -0.0083, -0.1356,  0.2026, -0.0505],
+                   [-0.0027, -0.0069, -0.0027, -0.2187, -0.0505,  0.2815]])
+    # fmt: on
+
+    L = nx.directed_combinatorial_laplacian_matrix(G, alpha=0.9, nodelist=sorted(G))
+    np.testing.assert_almost_equal(L, GL, decimal=3)
+
+    # Make the graph strongly connected, so we can use a random and lazy walk
+    G.add_edges_from(((2, 5), (6, 1)))
+
+    # fmt: off
+    GL = np.array([[ 0.1395, -0.0349, -0.0465,  0.    ,  0.    , -0.0581],
+                   [-0.0349,  0.093 , -0.0116,  0.    , -0.0465,  0.    ],
+                   [-0.0465, -0.0116,  0.0698,  0.    , -0.0116,  0.    ],
+                   [ 0.    ,  0.    ,  0.    ,  0.2326, -0.1163, -0.1163],
+                   [ 0.    , -0.0465, -0.0116, -0.1163,  0.2326, -0.0581],
+                   [-0.0581,  0.    ,  0.    , -0.1163, -0.0581,  0.2326]])
+    # fmt: on
+
+    L = nx.directed_combinatorial_laplacian_matrix(
+        G, alpha=0.9, nodelist=sorted(G), walk_type="random"
+    )
+    np.testing.assert_almost_equal(L, GL, decimal=3)
+
+    # fmt: off
+    GL = np.array([[ 0.0698, -0.0174, -0.0233,  0.    ,  0.    , -0.0291],
+                   [-0.0174,  0.0465, -0.0058,  0.    , -0.0233,  0.    ],
+                   [-0.0233, -0.0058,  0.0349,  0.    , -0.0058,  0.    ],
+                   [ 0.    ,  0.    ,  0.    ,  0.1163, -0.0581, -0.0581],
+                   [ 0.    , -0.0233, -0.0058, -0.0581,  0.1163, -0.0291],
+                   [-0.0291,  0.    ,  0.    , -0.0581, -0.0291,  0.1163]])
+    # fmt: on
+
+    L = nx.directed_combinatorial_laplacian_matrix(
+        G, alpha=0.9, nodelist=sorted(G), walk_type="lazy"
+    )
+    np.testing.assert_almost_equal(L, GL, decimal=3)
+
+    E = nx.DiGraph(margulis_gabber_galil_graph(2))
+    L = nx.directed_combinatorial_laplacian_matrix(E)
+    # fmt: off
+    expected = np.array(
+        [[ 0.16666667, -0.08333333, -0.08333333,  0.        ],
+         [-0.08333333,  0.16666667,  0.        , -0.08333333],
+         [-0.08333333,  0.        ,  0.16666667, -0.08333333],
+         [ 0.        , -0.08333333, -0.08333333,  0.16666667]]
+    )
+    # fmt: on
+    np.testing.assert_almost_equal(L, expected, decimal=6)
+
+    with pytest.raises(nx.NetworkXError):
+        nx.directed_combinatorial_laplacian_matrix(G, walk_type="pagerank", alpha=100)
+    with pytest.raises(nx.NetworkXError):
+        nx.directed_combinatorial_laplacian_matrix(G, walk_type="silly")
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_modularity.py b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_modularity.py
new file mode 100644
index 00000000..9f94ff4d
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_modularity.py
@@ -0,0 +1,87 @@
+import pytest
+
+np = pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+import networkx as nx
+from networkx.generators.degree_seq import havel_hakimi_graph
+
+
+class TestModularity:
+    @classmethod
+    def setup_class(cls):
+        deg = [3, 2, 2, 1, 0]
+        cls.G = havel_hakimi_graph(deg)
+        # Graph used as an example in Sec. 4.1 of Langville and Meyer,
+        # "Google's PageRank and Beyond". (Used for test_directed_laplacian)
+        cls.DG = nx.DiGraph()
+        cls.DG.add_edges_from(
+            (
+                (1, 2),
+                (1, 3),
+                (3, 1),
+                (3, 2),
+                (3, 5),
+                (4, 5),
+                (4, 6),
+                (5, 4),
+                (5, 6),
+                (6, 4),
+            )
+        )
+
+    def test_modularity(self):
+        "Modularity matrix"
+        # fmt: off
+        B = np.array([[-1.125,  0.25,  0.25,  0.625,  0.],
+                      [0.25, -0.5,  0.5, -0.25,  0.],
+                      [0.25,  0.5, -0.5, -0.25,  0.],
+                      [0.625, -0.25, -0.25, -0.125,  0.],
+                      [0.,  0.,  0.,  0.,  0.]])
+        # fmt: on
+
+        permutation = [4, 0, 1, 2, 3]
+        np.testing.assert_equal(nx.modularity_matrix(self.G), B)
+        np.testing.assert_equal(
+            nx.modularity_matrix(self.G, nodelist=permutation),
+            B[np.ix_(permutation, permutation)],
+        )
+
+    def test_modularity_weight(self):
+        "Modularity matrix with weights"
+        # fmt: off
+        B = np.array([[-1.125,  0.25,  0.25,  0.625,  0.],
+                      [0.25, -0.5,  0.5, -0.25,  0.],
+                      [0.25,  0.5, -0.5, -0.25,  0.],
+                      [0.625, -0.25, -0.25, -0.125,  0.],
+                      [0.,  0.,  0.,  0.,  0.]])
+        # fmt: on
+
+        G_weighted = self.G.copy()
+        for n1, n2 in G_weighted.edges():
+            G_weighted.edges[n1, n2]["weight"] = 0.5
+        # The following test would fail in networkx 1.1
+        np.testing.assert_equal(nx.modularity_matrix(G_weighted), B)
+        # The following test that the modularity matrix get rescaled accordingly
+        np.testing.assert_equal(
+            nx.modularity_matrix(G_weighted, weight="weight"), 0.5 * B
+        )
+
+    def test_directed_modularity(self):
+        "Directed Modularity matrix"
+        # fmt: off
+        B = np.array([[-0.2,  0.6,  0.8, -0.4, -0.4, -0.4],
+                      [0.,  0.,  0.,  0.,  0.,  0.],
+                      [0.7,  0.4, -0.3, -0.6,  0.4, -0.6],
+                      [-0.2, -0.4, -0.2, -0.4,  0.6,  0.6],
+                      [-0.2, -0.4, -0.2,  0.6, -0.4,  0.6],
+                      [-0.1, -0.2, -0.1,  0.8, -0.2, -0.2]])
+        # fmt: on
+        node_permutation = [5, 1, 2, 3, 4, 6]
+        idx_permutation = [4, 0, 1, 2, 3, 5]
+        mm = nx.directed_modularity_matrix(self.DG, nodelist=sorted(self.DG))
+        np.testing.assert_equal(mm, B)
+        np.testing.assert_equal(
+            nx.directed_modularity_matrix(self.DG, nodelist=node_permutation),
+            B[np.ix_(idx_permutation, idx_permutation)],
+        )
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_spectrum.py b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_spectrum.py
new file mode 100644
index 00000000..e9101303
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/tests/test_spectrum.py
@@ -0,0 +1,71 @@
+import pytest
+
+np = pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+import networkx as nx
+from networkx.generators.degree_seq import havel_hakimi_graph
+
+
+class TestSpectrum:
+    @classmethod
+    def setup_class(cls):
+        deg = [3, 2, 2, 1, 0]
+        cls.G = havel_hakimi_graph(deg)
+        cls.P = nx.path_graph(3)
+        cls.WG = nx.Graph(
+            (u, v, {"weight": 0.5, "other": 0.3}) for (u, v) in cls.G.edges()
+        )
+        cls.WG.add_node(4)
+        cls.DG = nx.DiGraph()
+        nx.add_path(cls.DG, [0, 1, 2])
+
+    def test_laplacian_spectrum(self):
+        "Laplacian eigenvalues"
+        evals = np.array([0, 0, 1, 3, 4])
+        e = sorted(nx.laplacian_spectrum(self.G))
+        np.testing.assert_almost_equal(e, evals)
+        e = sorted(nx.laplacian_spectrum(self.WG, weight=None))
+        np.testing.assert_almost_equal(e, evals)
+        e = sorted(nx.laplacian_spectrum(self.WG))
+        np.testing.assert_almost_equal(e, 0.5 * evals)
+        e = sorted(nx.laplacian_spectrum(self.WG, weight="other"))
+        np.testing.assert_almost_equal(e, 0.3 * evals)
+
+    def test_normalized_laplacian_spectrum(self):
+        "Normalized Laplacian eigenvalues"
+        evals = np.array([0, 0, 0.7712864461218, 1.5, 1.7287135538781])
+        e = sorted(nx.normalized_laplacian_spectrum(self.G))
+        np.testing.assert_almost_equal(e, evals)
+        e = sorted(nx.normalized_laplacian_spectrum(self.WG, weight=None))
+        np.testing.assert_almost_equal(e, evals)
+        e = sorted(nx.normalized_laplacian_spectrum(self.WG))
+        np.testing.assert_almost_equal(e, evals)
+        e = sorted(nx.normalized_laplacian_spectrum(self.WG, weight="other"))
+        np.testing.assert_almost_equal(e, evals)
+
+    def test_adjacency_spectrum(self):
+        "Adjacency eigenvalues"
+        evals = np.array([-np.sqrt(2), 0, np.sqrt(2)])
+        e = sorted(nx.adjacency_spectrum(self.P))
+        np.testing.assert_almost_equal(e, evals)
+
+    def test_modularity_spectrum(self):
+        "Modularity eigenvalues"
+        evals = np.array([-1.5, 0.0, 0.0])
+        e = sorted(nx.modularity_spectrum(self.P))
+        np.testing.assert_almost_equal(e, evals)
+        # Directed modularity eigenvalues
+        evals = np.array([-0.5, 0.0, 0.0])
+        e = sorted(nx.modularity_spectrum(self.DG))
+        np.testing.assert_almost_equal(e, evals)
+
+    def test_bethe_hessian_spectrum(self):
+        "Bethe Hessian eigenvalues"
+        evals = np.array([0.5 * (9 - np.sqrt(33)), 4, 0.5 * (9 + np.sqrt(33))])
+        e = sorted(nx.bethe_hessian_spectrum(self.P, r=2))
+        np.testing.assert_almost_equal(e, evals)
+        # Collapses back to Laplacian:
+        e1 = sorted(nx.bethe_hessian_spectrum(self.P, r=1))
+        e2 = sorted(nx.laplacian_spectrum(self.P))
+        np.testing.assert_almost_equal(e1, e2)