Compute closeness centrality for nodes.
Closeness centrality [R157] of a node is the reciprocal of the
sum of the shortest path distances from
to all
other nodes.
Since the sum of distances depends on the number of nodes in the
graph, closeness is normalized by the sum of minimum possible
distances
.
where is the shortest-path distance between
and
,
and
is the number of nodes in the graph.
Notice that higher values of closeness indicate higher centrality.
Parameters : | G : graph
u : node, optional
distance : edge attribute key, optional (default=None)
normalized : bool, optional
|
---|---|
Returns : | nodes : dictionary
|
Notes
The closeness centrality is normalized to where
is the number of nodes in the connected part of graph
containing the node. If the graph is not completely connected,
this algorithm computes the closeness centrality for each
connected part separately.
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
[R157] | (1, 2) Freeman, L.C., 1979. Centrality in networks: I. Conceptual clarification. Social Networks 1, 215–239. http://www.soc.ucsb.edu/faculty/friedkin/Syllabi/Soc146/Freeman78.PDF |