two version of R2R are hereHEADmaster

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diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/core.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/core.py
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+"""
+Find the k-cores of a graph.
+
+The k-core is found by recursively pruning nodes with degrees less than k.
+
+See the following references for details:
+
+An O(m) Algorithm for Cores Decomposition of Networks
+Vladimir Batagelj and Matjaz Zaversnik, 2003.
+https://arxiv.org/abs/cs.DS/0310049
+
+Generalized Cores
+Vladimir Batagelj and Matjaz Zaversnik, 2002.
+https://arxiv.org/pdf/cs/0202039
+
+For directed graphs a more general notion is that of D-cores which
+looks at (k, l) restrictions on (in, out) degree. The (k, k) D-core
+is the k-core.
+
+D-cores: Measuring Collaboration of Directed Graphs Based on Degeneracy
+Christos Giatsidis, Dimitrios M. Thilikos, Michalis Vazirgiannis, ICDM 2011.
+http://www.graphdegeneracy.org/dcores_ICDM_2011.pdf
+
+Multi-scale structure and topological anomaly detection via a new network \
+statistic: The onion decomposition
+L. Hébert-Dufresne, J. A. Grochow, and A. Allard
+Scientific Reports 6, 31708 (2016)
+http://doi.org/10.1038/srep31708
+
+"""
+
+import networkx as nx
+
+__all__ = [
+    "core_number",
+    "k_core",
+    "k_shell",
+    "k_crust",
+    "k_corona",
+    "k_truss",
+    "onion_layers",
+]
+
+
+@nx.utils.not_implemented_for("multigraph")
+@nx._dispatchable
+def core_number(G):
+    """Returns the core number for each node.
+
+    A k-core is a maximal subgraph that contains nodes of degree k or more.
+
+    The core number of a node is the largest value k of a k-core containing
+    that node.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected or directed graph
+
+    Returns
+    -------
+    core_number : dictionary
+       A dictionary keyed by node to the core number.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If `G` is a multigraph or contains self loops.
+
+    Notes
+    -----
+    For directed graphs the node degree is defined to be the
+    in-degree + out-degree.
+
+    Examples
+    --------
+    >>> degrees = [0, 1, 2, 2, 2, 2, 3]
+    >>> H = nx.havel_hakimi_graph(degrees)
+    >>> nx.core_number(H)
+    {0: 1, 1: 2, 2: 2, 3: 2, 4: 1, 5: 2, 6: 0}
+    >>> G = nx.DiGraph()
+    >>> G.add_edges_from([(1, 2), (2, 1), (2, 3), (2, 4), (3, 4), (4, 3)])
+    >>> nx.core_number(G)
+    {1: 2, 2: 2, 3: 2, 4: 2}
+
+    References
+    ----------
+    .. [1] An O(m) Algorithm for Cores Decomposition of Networks
+       Vladimir Batagelj and Matjaz Zaversnik, 2003.
+       https://arxiv.org/abs/cs.DS/0310049
+    """
+    if nx.number_of_selfloops(G) > 0:
+        msg = (
+            "Input graph has self loops which is not permitted; "
+            "Consider using G.remove_edges_from(nx.selfloop_edges(G))."
+        )
+        raise nx.NetworkXNotImplemented(msg)
+    degrees = dict(G.degree())
+    # Sort nodes by degree.
+    nodes = sorted(degrees, key=degrees.get)
+    bin_boundaries = [0]
+    curr_degree = 0
+    for i, v in enumerate(nodes):
+        if degrees[v] > curr_degree:
+            bin_boundaries.extend([i] * (degrees[v] - curr_degree))
+            curr_degree = degrees[v]
+    node_pos = {v: pos for pos, v in enumerate(nodes)}
+    # The initial guess for the core number of a node is its degree.
+    core = degrees
+    nbrs = {v: list(nx.all_neighbors(G, v)) for v in G}
+    for v in nodes:
+        for u in nbrs[v]:
+            if core[u] > core[v]:
+                nbrs[u].remove(v)
+                pos = node_pos[u]
+                bin_start = bin_boundaries[core[u]]
+                node_pos[u] = bin_start
+                node_pos[nodes[bin_start]] = pos
+                nodes[bin_start], nodes[pos] = nodes[pos], nodes[bin_start]
+                bin_boundaries[core[u]] += 1
+                core[u] -= 1
+    return core
+
+
+def _core_subgraph(G, k_filter, k=None, core=None):
+    """Returns the subgraph induced by nodes passing filter `k_filter`.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       The graph or directed graph to process
+    k_filter : filter function
+       This function filters the nodes chosen. It takes three inputs:
+       A node of G, the filter's cutoff, and the core dict of the graph.
+       The function should return a Boolean value.
+    k : int, optional
+      The order of the core. If not specified use the max core number.
+      This value is used as the cutoff for the filter.
+    core : dict, optional
+      Precomputed core numbers keyed by node for the graph `G`.
+      If not specified, the core numbers will be computed from `G`.
+
+    """
+    if core is None:
+        core = core_number(G)
+    if k is None:
+        k = max(core.values())
+    nodes = (v for v in core if k_filter(v, k, core))
+    return G.subgraph(nodes).copy()
+
+
+@nx._dispatchable(preserve_all_attrs=True, returns_graph=True)
+def k_core(G, k=None, core_number=None):
+    """Returns the k-core of G.
+
+    A k-core is a maximal subgraph that contains nodes of degree `k` or more.
+
+    .. deprecated:: 3.3
+       `k_core` will not accept `MultiGraph` objects in version 3.5.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+      A graph or directed graph
+    k : int, optional
+      The order of the core. If not specified return the main core.
+    core_number : dictionary, optional
+      Precomputed core numbers for the graph G.
+
+    Returns
+    -------
+    G : NetworkX graph
+      The k-core subgraph
+
+    Raises
+    ------
+    NetworkXNotImplemented
+      The k-core is not defined for multigraphs or graphs with self loops.
+
+    Notes
+    -----
+    The main core is the core with `k` as the largest core_number.
+
+    For directed graphs the node degree is defined to be the
+    in-degree + out-degree.
+
+    Graph, node, and edge attributes are copied to the subgraph.
+
+    Examples
+    --------
+    >>> degrees = [0, 1, 2, 2, 2, 2, 3]
+    >>> H = nx.havel_hakimi_graph(degrees)
+    >>> H.degree
+    DegreeView({0: 1, 1: 2, 2: 2, 3: 2, 4: 2, 5: 3, 6: 0})
+    >>> nx.k_core(H).nodes
+    NodeView((1, 2, 3, 5))
+
+    See Also
+    --------
+    core_number
+
+    References
+    ----------
+    .. [1] An O(m) Algorithm for Cores Decomposition of Networks
+       Vladimir Batagelj and Matjaz Zaversnik,  2003.
+       https://arxiv.org/abs/cs.DS/0310049
+    """
+
+    import warnings
+
+    if G.is_multigraph():
+        warnings.warn(
+            (
+                "\n\n`k_core` will not accept `MultiGraph` objects in version 3.5.\n"
+                "Convert it to an undirected graph instead, using::\n\n"
+                "\tG = nx.Graph(G)\n"
+            ),
+            category=DeprecationWarning,
+            stacklevel=5,
+        )
+
+    def k_filter(v, k, c):
+        return c[v] >= k
+
+    return _core_subgraph(G, k_filter, k, core_number)
+
+
+@nx._dispatchable(preserve_all_attrs=True, returns_graph=True)
+def k_shell(G, k=None, core_number=None):
+    """Returns the k-shell of G.
+
+    The k-shell is the subgraph induced by nodes with core number k.
+    That is, nodes in the k-core that are not in the (k+1)-core.
+
+    .. deprecated:: 3.3
+       `k_shell` will not accept `MultiGraph` objects in version 3.5.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+      A graph or directed graph.
+    k : int, optional
+      The order of the shell. If not specified return the outer shell.
+    core_number : dictionary, optional
+      Precomputed core numbers for the graph G.
+
+
+    Returns
+    -------
+    G : NetworkX graph
+       The k-shell subgraph
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        The k-shell is not implemented for multigraphs or graphs with self loops.
+
+    Notes
+    -----
+    This is similar to k_corona but in that case only neighbors in the
+    k-core are considered.
+
+    For directed graphs the node degree is defined to be the
+    in-degree + out-degree.
+
+    Graph, node, and edge attributes are copied to the subgraph.
+
+    Examples
+    --------
+    >>> degrees = [0, 1, 2, 2, 2, 2, 3]
+    >>> H = nx.havel_hakimi_graph(degrees)
+    >>> H.degree
+    DegreeView({0: 1, 1: 2, 2: 2, 3: 2, 4: 2, 5: 3, 6: 0})
+    >>> nx.k_shell(H, k=1).nodes
+    NodeView((0, 4))
+
+    See Also
+    --------
+    core_number
+    k_corona
+
+
+    References
+    ----------
+    .. [1] A model of Internet topology using k-shell decomposition
+       Shai Carmi, Shlomo Havlin, Scott Kirkpatrick, Yuval Shavitt,
+       and Eran Shir, PNAS  July 3, 2007   vol. 104  no. 27  11150-11154
+       http://www.pnas.org/content/104/27/11150.full
+    """
+
+    import warnings
+
+    if G.is_multigraph():
+        warnings.warn(
+            (
+                "\n\n`k_shell` will not accept `MultiGraph` objects in version 3.5.\n"
+                "Convert it to an undirected graph instead, using::\n\n"
+                "\tG = nx.Graph(G)\n"
+            ),
+            category=DeprecationWarning,
+            stacklevel=5,
+        )
+
+    def k_filter(v, k, c):
+        return c[v] == k
+
+    return _core_subgraph(G, k_filter, k, core_number)
+
+
+@nx._dispatchable(preserve_all_attrs=True, returns_graph=True)
+def k_crust(G, k=None, core_number=None):
+    """Returns the k-crust of G.
+
+    The k-crust is the graph G with the edges of the k-core removed
+    and isolated nodes found after the removal of edges are also removed.
+
+    .. deprecated:: 3.3
+       `k_crust` will not accept `MultiGraph` objects in version 3.5.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       A graph or directed graph.
+    k : int, optional
+      The order of the shell. If not specified return the main crust.
+    core_number : dictionary, optional
+      Precomputed core numbers for the graph G.
+
+    Returns
+    -------
+    G : NetworkX graph
+       The k-crust subgraph
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        The k-crust is not implemented for multigraphs or graphs with self loops.
+
+    Notes
+    -----
+    This definition of k-crust is different than the definition in [1]_.
+    The k-crust in [1]_ is equivalent to the k+1 crust of this algorithm.
+
+    For directed graphs the node degree is defined to be the
+    in-degree + out-degree.
+
+    Graph, node, and edge attributes are copied to the subgraph.
+
+    Examples
+    --------
+    >>> degrees = [0, 1, 2, 2, 2, 2, 3]
+    >>> H = nx.havel_hakimi_graph(degrees)
+    >>> H.degree
+    DegreeView({0: 1, 1: 2, 2: 2, 3: 2, 4: 2, 5: 3, 6: 0})
+    >>> nx.k_crust(H, k=1).nodes
+    NodeView((0, 4, 6))
+
+    See Also
+    --------
+    core_number
+
+    References
+    ----------
+    .. [1] A model of Internet topology using k-shell decomposition
+       Shai Carmi, Shlomo Havlin, Scott Kirkpatrick, Yuval Shavitt,
+       and Eran Shir, PNAS  July 3, 2007   vol. 104  no. 27  11150-11154
+       http://www.pnas.org/content/104/27/11150.full
+    """
+
+    import warnings
+
+    if G.is_multigraph():
+        warnings.warn(
+            (
+                "\n\n`k_crust` will not accept `MultiGraph` objects in version 3.5.\n"
+                "Convert it to an undirected graph instead, using::\n\n"
+                "\tG = nx.Graph(G)\n"
+            ),
+            category=DeprecationWarning,
+            stacklevel=5,
+        )
+
+    # Default for k is one less than in _core_subgraph, so just inline.
+    #    Filter is c[v] <= k
+    if core_number is None:
+        core_number = nx.core_number(G)
+    if k is None:
+        k = max(core_number.values()) - 1
+    nodes = (v for v in core_number if core_number[v] <= k)
+    return G.subgraph(nodes).copy()
+
+
+@nx._dispatchable(preserve_all_attrs=True, returns_graph=True)
+def k_corona(G, k, core_number=None):
+    """Returns the k-corona of G.
+
+    The k-corona is the subgraph of nodes in the k-core which have
+    exactly k neighbors in the k-core.
+
+    .. deprecated:: 3.3
+       `k_corona` will not accept `MultiGraph` objects in version 3.5.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       A graph or directed graph
+    k : int
+       The order of the corona.
+    core_number : dictionary, optional
+       Precomputed core numbers for the graph G.
+
+    Returns
+    -------
+    G : NetworkX graph
+       The k-corona subgraph
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        The k-corona is not defined for multigraphs or graphs with self loops.
+
+    Notes
+    -----
+    For directed graphs the node degree is defined to be the
+    in-degree + out-degree.
+
+    Graph, node, and edge attributes are copied to the subgraph.
+
+    Examples
+    --------
+    >>> degrees = [0, 1, 2, 2, 2, 2, 3]
+    >>> H = nx.havel_hakimi_graph(degrees)
+    >>> H.degree
+    DegreeView({0: 1, 1: 2, 2: 2, 3: 2, 4: 2, 5: 3, 6: 0})
+    >>> nx.k_corona(H, k=2).nodes
+    NodeView((1, 2, 3, 5))
+
+    See Also
+    --------
+    core_number
+
+    References
+    ----------
+    .. [1]  k -core (bootstrap) percolation on complex networks:
+       Critical phenomena and nonlocal effects,
+       A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes,
+       Phys. Rev. E 73, 056101 (2006)
+       http://link.aps.org/doi/10.1103/PhysRevE.73.056101
+    """
+
+    import warnings
+
+    if G.is_multigraph():
+        warnings.warn(
+            (
+                "\n\n`k_corona` will not accept `MultiGraph` objects in version 3.5.\n"
+                "Convert it to an undirected graph instead, using::\n\n"
+                "\tG = nx.Graph(G)\n"
+            ),
+            category=DeprecationWarning,
+            stacklevel=5,
+        )
+
+    def func(v, k, c):
+        return c[v] == k and k == sum(1 for w in G[v] if c[w] >= k)
+
+    return _core_subgraph(G, func, k, core_number)
+
+
+@nx.utils.not_implemented_for("directed")
+@nx.utils.not_implemented_for("multigraph")
+@nx._dispatchable(preserve_all_attrs=True, returns_graph=True)
+def k_truss(G, k):
+    """Returns the k-truss of `G`.
+
+    The k-truss is the maximal induced subgraph of `G` which contains at least
+    three vertices where every edge is incident to at least `k-2` triangles.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+      An undirected graph
+    k : int
+      The order of the truss
+
+    Returns
+    -------
+    H : NetworkX graph
+      The k-truss subgraph
+
+    Raises
+    ------
+    NetworkXNotImplemented
+      If `G` is a multigraph or directed graph or if it contains self loops.
+
+    Notes
+    -----
+    A k-clique is a (k-2)-truss and a k-truss is a (k+1)-core.
+
+    Graph, node, and edge attributes are copied to the subgraph.
+
+    K-trusses were originally defined in [2] which states that the k-truss
+    is the maximal induced subgraph where each edge belongs to at least
+    `k-2` triangles. A more recent paper, [1], uses a slightly different
+    definition requiring that each edge belong to at least `k` triangles.
+    This implementation uses the original definition of `k-2` triangles.
+
+    Examples
+    --------
+    >>> degrees = [0, 1, 2, 2, 2, 2, 3]
+    >>> H = nx.havel_hakimi_graph(degrees)
+    >>> H.degree
+    DegreeView({0: 1, 1: 2, 2: 2, 3: 2, 4: 2, 5: 3, 6: 0})
+    >>> nx.k_truss(H, k=2).nodes
+    NodeView((0, 1, 2, 3, 4, 5))
+
+    References
+    ----------
+    .. [1] Bounds and Algorithms for k-truss. Paul Burkhardt, Vance Faber,
+       David G. Harris, 2018. https://arxiv.org/abs/1806.05523v2
+    .. [2] Trusses: Cohesive Subgraphs for Social Network Analysis. Jonathan
+       Cohen, 2005.
+    """
+    if nx.number_of_selfloops(G) > 0:
+        msg = (
+            "Input graph has self loops which is not permitted; "
+            "Consider using G.remove_edges_from(nx.selfloop_edges(G))."
+        )
+        raise nx.NetworkXNotImplemented(msg)
+
+    H = G.copy()
+
+    n_dropped = 1
+    while n_dropped > 0:
+        n_dropped = 0
+        to_drop = []
+        seen = set()
+        for u in H:
+            nbrs_u = set(H[u])
+            seen.add(u)
+            new_nbrs = [v for v in nbrs_u if v not in seen]
+            for v in new_nbrs:
+                if len(nbrs_u & set(H[v])) < (k - 2):
+                    to_drop.append((u, v))
+        H.remove_edges_from(to_drop)
+        n_dropped = len(to_drop)
+        H.remove_nodes_from(list(nx.isolates(H)))
+
+    return H
+
+
+@nx.utils.not_implemented_for("multigraph")
+@nx.utils.not_implemented_for("directed")
+@nx._dispatchable
+def onion_layers(G):
+    """Returns the layer of each vertex in an onion decomposition of the graph.
+
+    The onion decomposition refines the k-core decomposition by providing
+    information on the internal organization of each k-shell. It is usually
+    used alongside the `core numbers`.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected graph without self loops.
+
+    Returns
+    -------
+    od_layers : dictionary
+        A dictionary keyed by node to the onion layer. The layers are
+        contiguous integers starting at 1.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If `G` is a multigraph or directed graph or if it contains self loops.
+
+    Examples
+    --------
+    >>> degrees = [0, 1, 2, 2, 2, 2, 3]
+    >>> H = nx.havel_hakimi_graph(degrees)
+    >>> H.degree
+    DegreeView({0: 1, 1: 2, 2: 2, 3: 2, 4: 2, 5: 3, 6: 0})
+    >>> nx.onion_layers(H)
+    {6: 1, 0: 2, 4: 3, 1: 4, 2: 4, 3: 4, 5: 4}
+
+    See Also
+    --------
+    core_number
+
+    References
+    ----------
+    .. [1] Multi-scale structure and topological anomaly detection via a new
+       network statistic: The onion decomposition
+       L. Hébert-Dufresne, J. A. Grochow, and A. Allard
+       Scientific Reports 6, 31708 (2016)
+       http://doi.org/10.1038/srep31708
+    .. [2] Percolation and the effective structure of complex networks
+       A. Allard and L. Hébert-Dufresne
+       Physical Review X 9, 011023 (2019)
+       http://doi.org/10.1103/PhysRevX.9.011023
+    """
+    if nx.number_of_selfloops(G) > 0:
+        msg = (
+            "Input graph contains self loops which is not permitted; "
+            "Consider using G.remove_edges_from(nx.selfloop_edges(G))."
+        )
+        raise nx.NetworkXNotImplemented(msg)
+    # Dictionaries to register the k-core/onion decompositions.
+    od_layers = {}
+    # Adjacency list
+    neighbors = {v: list(nx.all_neighbors(G, v)) for v in G}
+    # Effective degree of nodes.
+    degrees = dict(G.degree())
+    # Performs the onion decomposition.
+    current_core = 1
+    current_layer = 1
+    # Sets vertices of degree 0 to layer 1, if any.
+    isolated_nodes = list(nx.isolates(G))
+    if len(isolated_nodes) > 0:
+        for v in isolated_nodes:
+            od_layers[v] = current_layer
+            degrees.pop(v)
+        current_layer = 2
+    # Finds the layer for the remaining nodes.
+    while len(degrees) > 0:
+        # Sets the order for looking at nodes.
+        nodes = sorted(degrees, key=degrees.get)
+        # Sets properly the current core.
+        min_degree = degrees[nodes[0]]
+        if min_degree > current_core:
+            current_core = min_degree
+        # Identifies vertices in the current layer.
+        this_layer = []
+        for n in nodes:
+            if degrees[n] > current_core:
+                break
+            this_layer.append(n)
+        # Identifies the core/layer of the vertices in the current layer.
+        for v in this_layer:
+            od_layers[v] = current_layer
+            for n in neighbors[v]:
+                neighbors[n].remove(v)
+                degrees[n] = degrees[n] - 1
+            degrees.pop(v)
+        # Updates the layer count.
+        current_layer = current_layer + 1
+    # Returns the dictionaries containing the onion layer of each vertices.
+    return od_layers