gives a list of closeness centralities for the vertices in the graph g.
uses rules vw to specify the graph g.
- ClosenessCentrality will give high centralities to vertices that are at a short average distance to every other reachable vertex.
- ClosenessCentrality for a graph is given by , where is the average distance from vertex to all other vertices connected to .
- If is the distance matrix, then the average distance from vertex to all connected vertices is given by , where the sum is taken over all finite and is the number of vertices connected to .
- The closeness centrality for isolated vertices is taken to be zero.
- ClosenessCentrality works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.
Examplesopen allclose all
Basic Examples (2)
Highlight the closeness centrality for CycleGraph:
A computer ad hoc network can be modeled with a SpatialGraphDistribution. Find computers that can facilitate the quick spread of viruses in an infected network:
A directed network that describes the flow of information among 10 organizations concerned with social welfare issues in one midwestern US city. Find the organization that can most efficiently communicate with every other organization:
Properties & Relations (4)
ClosenessCentrality is the inverse of the average distances to other reachable vertices:
Use VertexIndex to obtain the centrality of a specific vertex:
Wolfram Research (2010), ClosenessCentrality, Wolfram Language function, https://reference.wolfram.com/language/ref/ClosenessCentrality.html (updated 2015).
Wolfram Language. 2010. "ClosenessCentrality." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/ClosenessCentrality.html.
Wolfram Language. (2010). ClosenessCentrality. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ClosenessCentrality.html