# Copyright (C) 2015 by
# Alessandro Luongo
# BSD license.
#
# 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 [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
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.
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 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)}