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CommunityModularity


gives the community modularity of a partition.

gives the community modularity of an assignment.
  • 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 V be partitioned into k subsets such that each subset belongs to one community. The community modularity Q of this partition is defined as
  • where is the percentage of number of edges that has both ends in community , and is the percentage of edges that start from community . In other words,
  • and
  • .
  • The community modularity Q 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
This defines a small graph:
This gives the community modularity, assuming a partition :
This gives the community modularity, assuming a partition :
This defines a small graph:
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This gives the community modularity, assuming a partition :
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This gives the community modularity, assuming a partition :
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This defines a graph with edge weights:
The community modularity of partition , ignoring edge weights:
The community modularity of partition , taking into account edge weights:
When taking into account edge weights, partition has higher community modularity: