networkx.algorithms.centrality.harmonic_centrality¶

harmonic_centrality(G, nbunch=None, distance=None)[source]

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

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

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 of nodes with harmonic centrality as the value.

Return type

dictionary

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.