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Closeness is a radial measure of centrality that favors actors who are connected with many others via short paths. Intuitively, if the graph represents a transportation network, then a node with high closeness would make a good location for a warehouse since the average distance to all other locations (i.e., all other nodes in the graph) is relatively short. In information-spreading networks, a node with high closeness centrality would be a good choice to start a rumor since many others can be reached with relatively few intermediates.

Definition (simple case)

On directed, unweighted graphs that are strongly connected, the closeness centrality of a node is defined as


where denotes the length of a shortest directed path from to . The definition for connected undirected graphs is identical with being defined as the length of a shortest path.


Special cases

Unconnected graphs

Edge weights and distances

If a link strength has been selected, the length of an -path is the sum of the corresponding attribute values of all links in the path.

Implementation in visone

Normalization and treatment of special cases

Algorithmic runtime

Related measures