harmonic_centrality¶

harmonic_centrality(G, nbunch=None, distance=None, sources=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.

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.