/usr/lib/python3/dist-packages/networkx/algorithms/centrality/harmonic.py is in python3-networkx 1.11-1ubuntu2.
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Harmonic centrality measure.
"""
# Copyright (C) 2015 by
# Alessandro Luongo
# BSD license.
from __future__ import division
import functools
import networkx as nx
__author__ = "\n".join(['Alessandro Luongo (alessandro.luongo@studenti.unimi.it'])
__all__ = ['harmonic_centrality']
def harmonic_centrality(G, distance=None):
r"""Compute harmonic centrality for nodes.
Harmonic centrality [1]_ of a node `u` is the sum of the reciprocal
of the shortest path distances from all other nodes to `u`
.. math::
C(u) = \sum_{v \neq u} \frac{1}{d(v, u)}
where `d(v, u)` is the shortest-path distance between `v` and `u`.
Notice that higher values indicate higher centrality.
Parameters
----------
G : graph
A NetworkX graph
distance : edge attribute key, optional (default=None)
Use the specified edge attribute as the edge distance in shortest
path calculations. If `None`, then each edge will have distance equal to 1.
Returns
-------
nodes : dictionary
Dictionary of nodes with harmonic centrality as the value.
See Also
--------
betweenness_centrality, load_centrality, eigenvector_centrality,
degree_centrality, closeness_centrality
Notes
-----
If the 'distance' keyword is set to an edge attribute key then the
shortest-path length will be computed using Dijkstra's algorithm with
that edge attribute as the edge weight.
References
----------
.. [1] Boldi, Paolo, and Sebastiano Vigna. "Axioms for centrality." Internet Mathematics 10.3-4 (2014): 222-262.
"""
if distance is not None:
# use Dijkstra's algorithm with specified attribute as edge weight
path_length = functools.partial(nx.all_pairs_dijkstra_path_length,
weight=distance)
else:
path_length = nx.all_pairs_shortest_path_length
nodes = G.nodes()
harmonic_centrality = {}
if len(G) <= 1:
for singleton in nodes:
harmonic_centrality[singleton] = 0.0
return harmonic_centrality
sp = path_length(G.reverse() if G.is_directed() else G)
for n in nodes:
harmonic_centrality[n] = sum([1/i if i > 0 else 0 for i in sp[n].values()])
return harmonic_centrality
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