CommunityModularity

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. >>


gives the community modularity of a partition.


gives the community modularity of an assignment.

DetailsDetails

  • CommunityModularity functionality is now available in the built-in Wolfram Language function GraphAssortativity.
  • To use , you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
  • A community in a network is a group of vertices such that there is a higher density of edges within the group than between them.
  • Given a graph , let the vertex set be partitioned into subsets such that each subset belongs to one community. The community modularity of this partition is defined as , where is the percentage of edges that have both ends in community , and is the percentage of edges that start from community . In other words, and .
  • The community modularity is a number less than or equal to 1. A large positive value indicates that the vertex partition gives significant community structure.
  • The following option can be given:
  • WeightedFalsewhether edges with higher weights are preferred during matching

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

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This gives the community modularity, assuming a partition :

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has been superseded by GraphAssortativity:

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