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GRAPH UTILITIES PACKAGE SYMBOL
CommunityModularity
gives the community modularity of a partition.
gives the community modularity of an assignment.
Details
- 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:
-
Weighted False whether edges with higher weights are preferred during matching
