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Closeness (graph theory)
Closeness is a centrality measure of a vertex within a graph. Vertices that are 'shallow' to other vertices (that is, those that tend to have short geodesic distances to other vertices with in the graph) have higher closeness. Closeness is preferred in network analysis to mean shortest-path length, as it gives higher values to more central vertices, and so is usually positively associated with other measures such as degree.
Definition
The closeness CC(v) for a vertex v is the reciprocal of the sum of geodesic distances to all other vertices in the graph.
See also
References
Sabidussi, G. (1966) The centrality index of a graph. Pyschometrika 31, 581--603.
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details