gives the community modularity of a partition.
gives the community modularity of an assignment.
Details and Options
- CommunityModularity functionality is now available in the built-in Wolfram Language function GraphAssortativity.
- To use CommunityModularity, 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:
Weighted False whether edges with higher weights are preferred during matching
Examplesopen allclose all
Basic Examples (2)
CommunityModularity has been superseded by GraphAssortativity:
Wolfram Research (2007), CommunityModularity, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/CommunityModularity.html.
Wolfram Language. 2007. "CommunityModularity." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/GraphUtilities/ref/CommunityModularity.html.
Wolfram Language. (2007). CommunityModularity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/GraphUtilities/ref/CommunityModularity.html