GraphUtilities`
GraphUtilities`

# CommunityModularity

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

CommunityModularity[g,partition]

gives the community modularity of a partition.

CommunityModularity[g,assignment]

gives the community modularity of an assignment.

# Details

• 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

# Examples

open allclose all

## Basic Examples(2)

This defines a small graph:

This gives the community modularity, assuming a partition {{1,2,3},{4,5,6}}:

CommunityModularity has been superseded by GraphAssortativity:

## Options(1)

### Weighted(1)

This defines a graph with edge weights:

The community modularity of partition {{1,2},{3,4}}, ignoring edge weights:

The community modularity of partition {{1,2},{3,4}}, taking into account edge weights:

When taking into account edge weights, partition {{1,4},{2,3}} has higher community modularity: