### view env/lib/python3.9/site-packages/networkx/algorithms/centrality/current_flow_closeness.py @ 0:4f3585e2f14bdraftdefaulttip

author shellac Mon, 22 Mar 2021 18:12:50 +0000
line wrap: on
line source
```
"""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 (
CGInverseLaplacian,
FullInverseLaplacian,
laplacian_sparse_matrix,
SuperLUInverseLaplacian,
)

__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.

--------
closeness_centrality

Notes
-----
The algorithm is from Brandes [1]_.

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
"""
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 {ordering[k]: float(v) for k, v in betweenness.items()}

information_centrality = current_flow_closeness_centrality
```