Note on the equivalence of the label propagation method of community detection and a Potts model approach

TL;DR

This paper demonstrates that label propagation for community detection is equivalent to a Potts model approach, revealing a large number of local minima and highlighting challenges in community aggregation.

Contribution

It establishes the equivalence between label propagation and a Potts model, providing new insights into the method's optimization landscape.

Findings

Number of local minima exceeds number of nodes

Aggregation tends to fragment communities

High complexity of the solution space

Abstract

We show that the recently introduced label propagation method for detecting communities in complex networks is equivalent to find the local minima of a simple Potts model. Applying to empirical data, the number of such local minima was found to be very high, much larger than the number of nodes in the graph. The aggregation method for combining information from more local minima shows a tendency to fragment the communities into very small pieces.