GRAPH UTILITIES PACKAGE SYMBOL

# CommunityModularity

gives the community modularity of a partition.

gives the community modularity of an assignment.

## DetailsDetails

• 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

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

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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