annotate env/lib/python3.9/site-packages/networkx/algorithms/centrality/current_flow_betweenness_subset.py @ 0:4f3585e2f14b draft default tip

"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

"""Current-flow betweenness centrality measures for subsets of nodes."""
import networkx as nx
from networkx.algorithms.centrality.flow_matrix import flow_matrix_row
from networkx.utils import not_implemented_for, reverse_cuthill_mckee_ordering

__all__ = [
    "current_flow_betweenness_centrality_subset",
    "edge_current_flow_betweenness_centrality_subset",
]


@not_implemented_for("directed")
def current_flow_betweenness_centrality_subset(
    G, sources, targets, normalized=True, weight=None, dtype=float, solver="lu"
):
    r"""Compute current-flow betweenness centrality for subsets of nodes.

    Current-flow betweenness centrality uses an electrical current
    model for information spreading in contrast to betweenness
    centrality which uses shortest paths.

    Current-flow betweenness centrality is also known as
    random-walk betweenness centrality [2]_.

    Parameters
    ----------
    G : graph
      A NetworkX graph

    sources: list of nodes
      Nodes to use as sources for current

    targets: list of nodes
      Nodes to use as sinks for current

    normalized : bool, optional (default=True)
      If True the betweenness values are normalized by b=b/(n-1)(n-2) where
      n is the number of nodes in G.

    weight : string or None, optional (default=None)
      Key for edge data used as the edge weight.
      If None, then use 1 as each edge weight.

    dtype: data type (float)
      Default data type for internal matrices.
      Set to np.float32 for lower memory consumption.

    solver: string (default='lu')
       Type of linear solver to use for computing the flow matrix.
       Options are "full" (uses most memory), "lu" (recommended), and
       "cg" (uses least memory).

    Returns
    -------
    nodes : dictionary
       Dictionary of nodes with betweenness centrality as the value.

    See Also
    --------
    approximate_current_flow_betweenness_centrality
    betweenness_centrality
    edge_betweenness_centrality
    edge_current_flow_betweenness_centrality

    Notes
    -----
    Current-flow betweenness can be computed in $O(I(n-1)+mn \log n)$
    time [1]_, where $I(n-1)$ is the time needed to compute the
    inverse Laplacian.  For a full matrix this is $O(n^3)$ but using
    sparse methods you can achieve $O(nm{\sqrt k})$ where $k$ is the
    Laplacian matrix condition number.

    The space required is $O(nw)$ where $w$ is the width of the sparse
    Laplacian matrix.  Worse case is $w=n$ for $O(n^2)$.

    If the edges have a 'weight' attribute they will be used as
    weights in this algorithm.  Unspecified weights are set to 1.

    References
    ----------
    .. [1] Centrality Measures Based on Current Flow.
       Ulrik Brandes and Daniel Fleischer,
       Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05).
       LNCS 3404, pp. 533-544. Springer-Verlag, 2005.
       http://algo.uni-konstanz.de/publications/bf-cmbcf-05.pdf

    .. [2] A measure of betweenness centrality based on random walks,
       M. E. J. Newman, Social Networks 27, 39-54 (2005).
    """
    from networkx.utils import reverse_cuthill_mckee_ordering

    try:
        import numpy as np
    except ImportError as e:
        raise ImportError(
            "current_flow_betweenness_centrality requires NumPy ", "http://numpy.org/"
        ) from e
    if not nx.is_connected(G):
        raise nx.NetworkXError("Graph not connected.")
    n = G.number_of_nodes()
    ordering = list(reverse_cuthill_mckee_ordering(G))
    # make a copy with integer labels according to rcm ordering
    # this could be done without a copy if we really wanted to
    mapping = dict(zip(ordering, range(n)))
    H = nx.relabel_nodes(G, mapping)
    betweenness = dict.fromkeys(H, 0.0)  # b[v]=0 for v in H
    for row, (s, t) in flow_matrix_row(H, weight=weight, dtype=dtype, solver=solver):
        for ss in sources:
            i = mapping[ss]
            for tt in targets:
                j = mapping[tt]
                betweenness[s] += 0.5 * np.abs(row[i] - row[j])
                betweenness[t] += 0.5 * np.abs(row[i] - row[j])
    if normalized:
        nb = (n - 1.0) * (n - 2.0)  # normalization factor
    else:
        nb = 2.0
    for v in H:
        betweenness[v] = betweenness[v] / nb + 1.0 / (2 - n)
    return {ordering[k]: v for k, v in betweenness.items()}


@not_implemented_for("directed")
def edge_current_flow_betweenness_centrality_subset(
    G, sources, targets, normalized=True, weight=None, dtype=float, solver="lu"
):
    r"""Compute current-flow betweenness centrality for edges using subsets
    of nodes.

    Current-flow betweenness centrality uses an electrical current
    model for information spreading in contrast to betweenness
    centrality which uses shortest paths.

    Current-flow betweenness centrality is also known as
    random-walk betweenness centrality [2]_.

    Parameters
    ----------
    G : graph
      A NetworkX graph

    sources: list of nodes
      Nodes to use as sources for current

    targets: list of nodes
      Nodes to use as sinks for current

    normalized : bool, optional (default=True)
      If True the betweenness values are normalized by b=b/(n-1)(n-2) where
      n is the number of nodes in G.

    weight : string or None, optional (default=None)
      Key for edge data used as the edge weight.
      If None, then use 1 as each edge weight.

    dtype: data type (float)
      Default data type for internal matrices.
      Set to np.float32 for lower memory consumption.

    solver: string (default='lu')
       Type of linear solver to use for computing the flow matrix.
       Options are "full" (uses most memory), "lu" (recommended), and
       "cg" (uses least memory).

    Returns
    -------
    nodes : dict
       Dictionary of edge tuples with betweenness centrality as the value.

    See Also
    --------
    betweenness_centrality
    edge_betweenness_centrality
    current_flow_betweenness_centrality

    Notes
    -----
    Current-flow betweenness can be computed in $O(I(n-1)+mn \log n)$
    time [1]_, where $I(n-1)$ is the time needed to compute the
    inverse Laplacian.  For a full matrix this is $O(n^3)$ but using
    sparse methods you can achieve $O(nm{\sqrt k})$ where $k$ is the
    Laplacian matrix condition number.

    The space required is $O(nw)$ where $w$ is the width of the sparse
    Laplacian matrix.  Worse case is $w=n$ for $O(n^2)$.

    If the edges have a 'weight' attribute they will be used as
    weights in this algorithm.  Unspecified weights are set to 1.

    References
    ----------
    .. [1] Centrality Measures Based on Current Flow.
       Ulrik Brandes and Daniel Fleischer,
       Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05).
       LNCS 3404, pp. 533-544. Springer-Verlag, 2005.
       http://algo.uni-konstanz.de/publications/bf-cmbcf-05.pdf

    .. [2] A measure of betweenness centrality based on random walks,
       M. E. J. Newman, Social Networks 27, 39-54 (2005).
    """
    try:
        import numpy as np
    except ImportError as e:
        raise ImportError(
            "current_flow_betweenness_centrality requires NumPy " "http://numpy.org/"
        ) from e
    if not nx.is_connected(G):
        raise nx.NetworkXError("Graph not connected.")
    n = G.number_of_nodes()
    ordering = list(reverse_cuthill_mckee_ordering(G))
    # make a copy with integer labels according to rcm ordering
    # this could be done without a copy if we really wanted to
    mapping = dict(zip(ordering, range(n)))
    H = nx.relabel_nodes(G, mapping)
    edges = (tuple(sorted((u, v))) for u, v in H.edges())
    betweenness = dict.fromkeys(edges, 0.0)
    if normalized:
        nb = (n - 1.0) * (n - 2.0)  # normalization factor
    else:
        nb = 2.0
    for row, (e) in flow_matrix_row(H, weight=weight, dtype=dtype, solver=solver):
        for ss in sources:
            i = mapping[ss]
            for tt in targets:
                j = mapping[tt]
                betweenness[e] += 0.5 * np.abs(row[i] - row[j])
        betweenness[e] /= nb
    return {(ordering[s], ordering[t]): v for (s, t), v in betweenness.items()}