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This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# Source code for networkx.algorithms.centrality.harmonic

#    Copyright (C) 2015 by
#    Alessandro Luongo
#
# Authors:
#    Alessandro Luongo <alessandro.luongo@studenti.unimi.it>
#
"""Functions for computing the harmonic centrality of a graph."""
from __future__ import division
from functools import partial

import networkx as nx

__all__ = ['harmonic_centrality']

[docs]def harmonic_centrality(G, nbunch=None, distance=None):
r"""Compute harmonic centrality for nodes.

Harmonic centrality _ 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

nbunch : container
Container of nodes. If provided harmonic centrality will be computed
only over the nodes in nbunch.

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.

--------
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
----------
..  Boldi, Paolo, and Sebastiano Vigna. "Axioms for centrality."
Internet Mathematics 10.3-4 (2014): 222-262.
"""
if G.is_directed():
G = G.reverse()
spl = partial(nx.shortest_path_length, G, weight=distance)
return {u: sum(1 / d if d > 0 else 0 for v, d in spl(source=u).items())
for u in G.nbunch_iter(nbunch)}