/usr/lib/python3/dist-packages/networkx/algorithms/centrality/current_flow_betweenness_subset.py is in python3-networkx 1.9+dfsg1-1.
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Current-flow betweenness centrality measures for subsets of nodes.
"""
# Copyright (C) 2010-2011 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)"""
__all__ = ['current_flow_betweenness_centrality_subset',
'edge_current_flow_betweenness_centrality_subset']
import itertools
import networkx as nx
from networkx.algorithms.centrality.flow_matrix import *
def current_flow_betweenness_centrality_subset(G,sources,targets,
normalized=True,
weight='weight',
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='weight')
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://www.inf.uni-konstanz.de/algo/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:
raise ImportError('current_flow_betweenness_centrality requires NumPy ',
'http://scipy.org/')
try:
import scipy
except ImportError:
raise ImportError('current_flow_betweenness_centrality requires SciPy ',
'http://scipy.org/')
if G.is_directed():
raise nx.NetworkXError('current_flow_betweenness_centrality() ',
'not defined for digraphs.')
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 dict((ordering[k],v) for k,v in betweenness.items())
def edge_current_flow_betweenness_centrality_subset(G, sources, targets,
normalized=True,
weight='weight',
dtype=float, solver='lu'):
"""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='weight')
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 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://www.inf.uni-konstanz.de/algo/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:
raise ImportError('current_flow_betweenness_centrality requires NumPy ',
'http://scipy.org/')
try:
import scipy
except ImportError:
raise ImportError('current_flow_betweenness_centrality requires SciPy ',
'http://scipy.org/')
if G.is_directed():
raise nx.NetworkXError('edge_current_flow_betweenness_centrality ',
'not defined for digraphs.')
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.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 dict(((ordering[s],ordering[t]),v)
for (s,t),v in betweenness.items())
# fixture for nose tests
def setup_module(module):
from nose import SkipTest
try:
import numpy
import scipy
except:
raise SkipTest("NumPy not available")
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