7.5.10.1. networkx.algorithms.centrality.harmonic_centrality¶

networkx.algorithms.centrality.harmonic_centrality(G, distance=None)[source]¶

Compute harmonic centrality for nodes.

Harmonic centrality [R539] of a node u is the sum of the reciprocal of the shortest path distances from all other nodes to u

\[C(u) = \sum_{v \neq u} \frac{1}{d(v, u)}\]

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 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

[R539]

(1, 2) Boldi, Paolo, and Sebastiano Vigna. “Axioms for centrality.” Internet Mathematics 10.3-4 (2014): 222-262.