Emerging communities in networks - a flow of ties

TL;DR

This paper introduces a flow-based method using differential equations for community detection in networks, demonstrated on signed graphs and fractal structures, effectively handling overlapping communities with added noise.

Contribution

It presents a novel flow method for community detection that interprets network dynamics through differential equations, including applications to signed graphs and fractal networks.

Findings

Effective partitioning of signed graphs into two communities.

Successful identification of communities in Sierpinski triangle structures.

Handling of overlapping nodes through noise addition.

Abstract

Algorithms for search of communities in networks usually consist discrete variations of links. Here we discuss a flow method, driven by a set of differential equations. Two examples are demonstrated in detail. First is a partition of a signed graph into two parts, where the proposed equations are interpreted in terms of removal of a cognitive dissonance by agents placed in the network nodes. There, the signs and values of links refer to positive or negative interpersonal relationships of different strength. Second is an application of a method akin to the previous one, dedicated to communities identification, to the Sierpinski triangle of finite size. During the time evolution, the related graphs are weighted; yet at the end the discrete character of links is restored. In the case of the Sierpinski triangle, the method is supplemented by adding a small noise to the initial connectivity matrix. By breaking the symmetry of the network, this allows to a successful handling of overlapping nodes.