Source code for networkx.algorithms.centrality.harmonic

"""Functions for computing the harmonic centrality of a graph."""
from functools import partial

import networkx as nx

__all__ = ["harmonic_centrality"]

[docs] @nx._dispatchable(edge_attrs="distance") def harmonic_centrality(G, nbunch=None, distance=None, sources=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`. If `sources` is given as an argument, the returned harmonic centrality values are calculated as the sum of the reciprocals of the shortest path distances from the nodes specified in `sources` to `u` instead of from all nodes to `u`. Notice that higher values indicate higher centrality. Parameters ---------- G : graph A NetworkX graph nbunch : container (default: all nodes in G) Container of nodes for which harmonic centrality values are calculated. sources : container (default: all nodes in G) Container of nodes `v` over which reciprocal distances are computed. Nodes not in `G` are silently ignored. 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. """ nbunch = set(G.nbunch_iter(nbunch)) if nbunch is not None else set(G.nodes) sources = set(G.nbunch_iter(sources)) if sources is not None else G.nodes spl = partial(nx.shortest_path_length, G, weight=distance) centrality = {u: 0 for u in nbunch} for v in sources: dist = spl(v) for u in nbunch.intersection(dist): d = dist[u] if d == 0: # handle u == v and edges with 0 weight continue centrality[u] += 1 / d return centrality