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## iof-tools / networkxMiCe / networkx-master / networkx / algorithms / centrality / harmonic.py @ 5cef0f13

 1 ```# Copyright (C) 2015 by ``` ```# Alessandro Luongo ``` ```# BSD license. ``` ```# ``` ```# Authors: ``` ```# Alessandro Luongo ``` ```# ``` ```"""Functions for computing the harmonic centrality of a graph.""" ``` ```from __future__ import division ``` ```from functools import partial ``` ```import networkx as nx ``` ```__all__ = ['harmonic_centrality'] ``` ```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)} ```