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Source code for networkx.algorithms.centrality.harmonic

#    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)}