Today I read a paper titled “On weakly optimal partitions in modular networks”
The abstract is:
Modularity was introduced as a measure of goodness for the community structure induced by a partition of the set of vertices in a graph.
Then, it also became an objective function used to find good partitions, with high success.
Nevertheless, some works have shown a scaling limit and certain instabilities when finding communities with this criterion.
Modularity has been studied proposing several formalisms, as hamiltonians in a Potts model or laplacians in spectral partitioning.
In this paper we present a new probabilistic formalism to analyze modularity, and from it we derive an algorithm based on weakly optimal partitions.
This algorithm obtains good quality partitions and also scales to large graphs.