two version of R2R are hereHEADmaster

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diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/cuts.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/cuts.py
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+"""Functions for finding and evaluating cuts in a graph."""
+
+from itertools import chain
+
+import networkx as nx
+
+__all__ = [
+    "boundary_expansion",
+    "conductance",
+    "cut_size",
+    "edge_expansion",
+    "mixing_expansion",
+    "node_expansion",
+    "normalized_cut_size",
+    "volume",
+]
+
+
+# TODO STILL NEED TO UPDATE ALL THE DOCUMENTATION!
+
+
+@nx._dispatchable(edge_attrs="weight")
+def cut_size(G, S, T=None, weight=None):
+    """Returns the size of the cut between two sets of nodes.
+
+    A *cut* is a partition of the nodes of a graph into two sets. The
+    *cut size* is the sum of the weights of the edges "between" the two
+    sets of nodes.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    S : collection
+        A collection of nodes in `G`.
+
+    T : collection
+        A collection of nodes in `G`. If not specified, this is taken to
+        be the set complement of `S`.
+
+    weight : object
+        Edge attribute key to use as weight. If not specified, edges
+        have weight one.
+
+    Returns
+    -------
+    number
+        Total weight of all edges from nodes in set `S` to nodes in
+        set `T` (and, in the case of directed graphs, all edges from
+        nodes in `T` to nodes in `S`).
+
+    Examples
+    --------
+    In the graph with two cliques joined by a single edges, the natural
+    bipartition of the graph into two blocks, one for each clique,
+    yields a cut of weight one::
+
+        >>> G = nx.barbell_graph(3, 0)
+        >>> S = {0, 1, 2}
+        >>> T = {3, 4, 5}
+        >>> nx.cut_size(G, S, T)
+        1
+
+    Each parallel edge in a multigraph is counted when determining the
+    cut size::
+
+        >>> G = nx.MultiGraph(["ab", "ab"])
+        >>> S = {"a"}
+        >>> T = {"b"}
+        >>> nx.cut_size(G, S, T)
+        2
+
+    Notes
+    -----
+    In a multigraph, the cut size is the total weight of edges including
+    multiplicity.
+
+    """
+    edges = nx.edge_boundary(G, S, T, data=weight, default=1)
+    if G.is_directed():
+        edges = chain(edges, nx.edge_boundary(G, T, S, data=weight, default=1))
+    return sum(weight for u, v, weight in edges)
+
+
+@nx._dispatchable(edge_attrs="weight")
+def volume(G, S, weight=None):
+    """Returns the volume of a set of nodes.
+
+    The *volume* of a set *S* is the sum of the (out-)degrees of nodes
+    in *S* (taking into account parallel edges in multigraphs). [1]
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    S : collection
+        A collection of nodes in `G`.
+
+    weight : object
+        Edge attribute key to use as weight. If not specified, edges
+        have weight one.
+
+    Returns
+    -------
+    number
+        The volume of the set of nodes represented by `S` in the graph
+        `G`.
+
+    See also
+    --------
+    conductance
+    cut_size
+    edge_expansion
+    edge_boundary
+    normalized_cut_size
+
+    References
+    ----------
+    .. [1] David Gleich.
+           *Hierarchical Directed Spectral Graph Partitioning*.
+           <https://www.cs.purdue.edu/homes/dgleich/publications/Gleich%202005%20-%20hierarchical%20directed%20spectral.pdf>
+
+    """
+    degree = G.out_degree if G.is_directed() else G.degree
+    return sum(d for v, d in degree(S, weight=weight))
+
+
+@nx._dispatchable(edge_attrs="weight")
+def normalized_cut_size(G, S, T=None, weight=None):
+    """Returns the normalized size of the cut between two sets of nodes.
+
+    The *normalized cut size* is the cut size times the sum of the
+    reciprocal sizes of the volumes of the two sets. [1]
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    S : collection
+        A collection of nodes in `G`.
+
+    T : collection
+        A collection of nodes in `G`.
+
+    weight : object
+        Edge attribute key to use as weight. If not specified, edges
+        have weight one.
+
+    Returns
+    -------
+    number
+        The normalized cut size between the two sets `S` and `T`.
+
+    Notes
+    -----
+    In a multigraph, the cut size is the total weight of edges including
+    multiplicity.
+
+    See also
+    --------
+    conductance
+    cut_size
+    edge_expansion
+    volume
+
+    References
+    ----------
+    .. [1] David Gleich.
+           *Hierarchical Directed Spectral Graph Partitioning*.
+           <https://www.cs.purdue.edu/homes/dgleich/publications/Gleich%202005%20-%20hierarchical%20directed%20spectral.pdf>
+
+    """
+    if T is None:
+        T = set(G) - set(S)
+    num_cut_edges = cut_size(G, S, T=T, weight=weight)
+    volume_S = volume(G, S, weight=weight)
+    volume_T = volume(G, T, weight=weight)
+    return num_cut_edges * ((1 / volume_S) + (1 / volume_T))
+
+
+@nx._dispatchable(edge_attrs="weight")
+def conductance(G, S, T=None, weight=None):
+    """Returns the conductance of two sets of nodes.
+
+    The *conductance* is the quotient of the cut size and the smaller of
+    the volumes of the two sets. [1]
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    S : collection
+        A collection of nodes in `G`.
+
+    T : collection
+        A collection of nodes in `G`.
+
+    weight : object
+        Edge attribute key to use as weight. If not specified, edges
+        have weight one.
+
+    Returns
+    -------
+    number
+        The conductance between the two sets `S` and `T`.
+
+    See also
+    --------
+    cut_size
+    edge_expansion
+    normalized_cut_size
+    volume
+
+    References
+    ----------
+    .. [1] David Gleich.
+           *Hierarchical Directed Spectral Graph Partitioning*.
+           <https://www.cs.purdue.edu/homes/dgleich/publications/Gleich%202005%20-%20hierarchical%20directed%20spectral.pdf>
+
+    """
+    if T is None:
+        T = set(G) - set(S)
+    num_cut_edges = cut_size(G, S, T, weight=weight)
+    volume_S = volume(G, S, weight=weight)
+    volume_T = volume(G, T, weight=weight)
+    return num_cut_edges / min(volume_S, volume_T)
+
+
+@nx._dispatchable(edge_attrs="weight")
+def edge_expansion(G, S, T=None, weight=None):
+    """Returns the edge expansion between two node sets.
+
+    The *edge expansion* is the quotient of the cut size and the smaller
+    of the cardinalities of the two sets. [1]
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    S : collection
+        A collection of nodes in `G`.
+
+    T : collection
+        A collection of nodes in `G`.
+
+    weight : object
+        Edge attribute key to use as weight. If not specified, edges
+        have weight one.
+
+    Returns
+    -------
+    number
+        The edge expansion between the two sets `S` and `T`.
+
+    See also
+    --------
+    boundary_expansion
+    mixing_expansion
+    node_expansion
+
+    References
+    ----------
+    .. [1] Fan Chung.
+           *Spectral Graph Theory*.
+           (CBMS Regional Conference Series in Mathematics, No. 92),
+           American Mathematical Society, 1997, ISBN 0-8218-0315-8
+           <http://www.math.ucsd.edu/~fan/research/revised.html>
+
+    """
+    if T is None:
+        T = set(G) - set(S)
+    num_cut_edges = cut_size(G, S, T=T, weight=weight)
+    return num_cut_edges / min(len(S), len(T))
+
+
+@nx._dispatchable(edge_attrs="weight")
+def mixing_expansion(G, S, T=None, weight=None):
+    """Returns the mixing expansion between two node sets.
+
+    The *mixing expansion* is the quotient of the cut size and twice the
+    number of edges in the graph. [1]
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    S : collection
+        A collection of nodes in `G`.
+
+    T : collection
+        A collection of nodes in `G`.
+
+    weight : object
+        Edge attribute key to use as weight. If not specified, edges
+        have weight one.
+
+    Returns
+    -------
+    number
+        The mixing expansion between the two sets `S` and `T`.
+
+    See also
+    --------
+    boundary_expansion
+    edge_expansion
+    node_expansion
+
+    References
+    ----------
+    .. [1] Vadhan, Salil P.
+           "Pseudorandomness."
+           *Foundations and Trends
+           in Theoretical Computer Science* 7.1–3 (2011): 1–336.
+           <https://doi.org/10.1561/0400000010>
+
+    """
+    num_cut_edges = cut_size(G, S, T=T, weight=weight)
+    num_total_edges = G.number_of_edges()
+    return num_cut_edges / (2 * num_total_edges)
+
+
+# TODO What is the generalization to two arguments, S and T? Does the
+# denominator become `min(len(S), len(T))`?
+@nx._dispatchable
+def node_expansion(G, S):
+    """Returns the node expansion of the set `S`.
+
+    The *node expansion* is the quotient of the size of the node
+    boundary of *S* and the cardinality of *S*. [1]
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    S : collection
+        A collection of nodes in `G`.
+
+    Returns
+    -------
+    number
+        The node expansion of the set `S`.
+
+    See also
+    --------
+    boundary_expansion
+    edge_expansion
+    mixing_expansion
+
+    References
+    ----------
+    .. [1] Vadhan, Salil P.
+           "Pseudorandomness."
+           *Foundations and Trends
+           in Theoretical Computer Science* 7.1–3 (2011): 1–336.
+           <https://doi.org/10.1561/0400000010>
+
+    """
+    neighborhood = set(chain.from_iterable(G.neighbors(v) for v in S))
+    return len(neighborhood) / len(S)
+
+
+# TODO What is the generalization to two arguments, S and T? Does the
+# denominator become `min(len(S), len(T))`?
+@nx._dispatchable
+def boundary_expansion(G, S):
+    """Returns the boundary expansion of the set `S`.
+
+    The *boundary expansion* is the quotient of the size
+    of the node boundary and the cardinality of *S*. [1]
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    S : collection
+        A collection of nodes in `G`.
+
+    Returns
+    -------
+    number
+        The boundary expansion of the set `S`.
+
+    See also
+    --------
+    edge_expansion
+    mixing_expansion
+    node_expansion
+
+    References
+    ----------
+    .. [1] Vadhan, Salil P.
+           "Pseudorandomness."
+           *Foundations and Trends in Theoretical Computer Science*
+           7.1–3 (2011): 1–336.
+           <https://doi.org/10.1561/0400000010>
+
+    """
+    return len(nx.node_boundary(G, S)) / len(S)