Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

# networkx.algorithms.centrality.harmonic_centrality¶

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

Compute harmonic centrality for nodes.

Harmonic centrality  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.

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
Ggraph

A NetworkX graph

nbunchcontainer (default: all nodes in G)

Container of nodes for which harmonic centrality values are calculated.

sourcescontainer (default: all nodes in G)

Container of nodes v over which reciprocal distances are computed. Nodes not in G are silently ignored.

distanceedge 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
nodesdictionary

Dictionary of nodes with harmonic centrality as the value.

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.