optimal.community: Optimal community structure

Description

This function calculates the optimal community structure of a graph, by maximizing the modularity measure over all possible partitions.

Usage

optimal.community(graph)

Arguments

graph

The input graph. Edge directions are ignored for directed graphs.

Value

optimal.community returns a communities object, please see the communities manual page for details.

concept

Community structure
Modularity

Details

This function calculates the optimal community structure for a graph, in terms of maximal modularity score. The calculation is done by transforming the modularity maximization into an integer programming problem, and then calling the GLPK library to solve that. Please the reference below for details.

Note that modularity optimization is an NP-complete problem, and all known algorithms for it have exponential time complexity. This means that you probably don't want to run this function on larger graphs. Graphs with up to fifty vertices should be fine, graphs with a couple of hundred vertices might be possible.

References

Ulrik Brandes, Daniel Delling, Marco Gaertler, Robert Gorke, Martin Hoefer, Zoran Nikoloski, Dorothea Wagner: On Modularity Clustering, IEEE Transactions on Knowledge and Data Engineering 20(2):172-188, 2008.

Examples

Run this code

## Zachary's karate club
g <- graph.famous("Zachary")

## We put everything into a big 'try' block, in case 
## igraph was compiled without GLPK support

try({
  ## The calculation only takes a couple of seconds
  oc <- optimal.community(g)

  ## Double check the result
  print(modularity(oc))
  print(modularity(g, membership(oc)))

  ## Compare to the greedy optimizer
  fc <- fastgreedy.community(g)
  print(modularity(fc))
}, silent=TRUE)

Run the code above in your browser using DataLab

Get 50% off unlimited learning