How to divide a fully connected graph into similar subgraphs?

Question

I have a complete graph with symmetric weights (think about a set of cities with travel distance as edge cost) and I want to split the vertices into a fixed number of disjoint sets so that a an error function is optimized. The error function could for example be the maximum of the mean or maximal distance within the subgraphs.

I think that this should be a not too unusual problem, but I am missing the right search term to find the right algorithms or software packages.

Answer 1

This area is called community detection or graph partitioning. Usually the methods are based on a specific objective function, but there are several possible algorithms that might let you optimize your own, depending on the type of function: the Kernighan–Lin algorithm , hierarchical maximization through the Louvain method .