Communities in networks - a continuous approach

TL;DR

This paper introduces a continuous dynamical system based on differential equations to identify communities in weighted networks without prior knowledge of the number of communities, demonstrating superior performance over modularity algorithms in certain cases.

Contribution

It presents a novel differential equation approach for community detection that does not require pre-specifying the number of communities.

Findings

Outperforms modularity algorithms for more than four communities

Successfully identifies block structures in noisy networks

Works without prior knowledge of the number of communities

Abstract

A system of differential equations is proposed designed as to identify communities in weighted networks. The input is a symmetric connectivity matrix $A_{ij}$. A priori information on the number of communities is not needed. To verify the dynamics, we prepared sets of separate, fully connected clusters. In this case, the matrix $A$ has a block structure of zeros and units. A noise is introduced as positive random numbers added to zeros and subtracted from units. The task of the dynamics is to reproduce the initial block structure. In this test, the system outperforms the modularity algorithm, if the number of clusters is larger than four.