107 lines
3.5 KiB
Python
107 lines
3.5 KiB
Python
# 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']
|
|
|
|
|
|
@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 pytest
|
|
def setup_module(module):
|
|
import pytest
|
|
numpy = pytest.importorskip('numpy')
|