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Source code for networkx.algorithms.centrality.current_flow_closeness

#    Copyright (C) 2010-2019 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
# Author: Aric Hagberg (hagberg@lanl.gov)
"""Current-flow closeness centrality measures."""
import networkx as nx

from networkx.utils import not_implemented_for, reverse_cuthill_mckee_ordering
from networkx.algorithms.centrality.flow_matrix import *

__all__ = ['current_flow_closeness_centrality', 'information_centrality']

[docs]@not_implemented_for('directed') def current_flow_closeness_centrality(G, weight=None, dtype=float, solver='lu'): """Compute current-flow closeness centrality for nodes. Current-flow closeness centrality is variant of closeness centrality based on effective resistance between nodes in a network. This metric is also known as information centrality. Parameters ---------- G : graph A NetworkX graph. weight : None or string, optional (default=None) If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight. dtype: data type (default=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 current flow closeness centrality as the value. See Also -------- closeness_centrality Notes ----- The algorithm is from Brandes [1]_. See also [2]_ for the original definition of information centrality. References ---------- .. [1] Ulrik Brandes and Daniel Fleischer, Centrality Measures Based on Current Flow. 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] Karen Stephenson and Marvin Zelen: Rethinking centrality: Methods and examples. Social Networks 11(1):1-37, 1989. https://doi.org/10.1016/0378-8733(89)90016-6 """ import numpy as np import scipy if not nx.is_connected(G): raise nx.NetworkXError("Graph not connected.") solvername = {"full": FullInverseLaplacian, "lu": SuperLUInverseLaplacian, "cg": CGInverseLaplacian} 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 H = nx.relabel_nodes(G, dict(zip(ordering, range(n)))) betweenness = dict.fromkeys(H, 0.0) # b[v]=0 for v in H n = H.number_of_nodes() L = laplacian_sparse_matrix(H, nodelist=range(n), weight=weight, dtype=dtype, format='csc') C2 = solvername[solver](L, width=1, dtype=dtype) # initialize solver for v in H: col = C2.get_row(v) for w in H: betweenness[v] += col[v] - 2 * col[w] betweenness[w] += col[v] for v in H: betweenness[v] = 1.0 / (betweenness[v]) return dict((ordering[k], float(v)) for k, v in betweenness.items())
information_centrality = current_flow_closeness_centrality # fixture for nose tests def setup_module(module): from nose import SkipTest try: import numpy except: raise SkipTest("NumPy not available")