Random field Ising model and community structure in complex networks

TL;DR

This paper introduces a novel method using a random field Ising model's ground state to detect community structures in complex networks, leveraging combinatorial optimization for exact solutions.

Contribution

The paper presents a new approach linking Ising model ground states to community detection, applicable to both weighted and unweighted networks, with exact numerical solutions.

Findings

Successfully applied to various real-world networks

Provides a criterion for community existence

Works for weighted and unweighted networks

Abstract

We propose a method to find out the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field $B_s = +\infty$, $B_{t} = -\infty$, and $B_{i\neq s,t}=0$ for a node pair $s$ and $t$. The ground state problem is equivalent to the so-called maximum flow problem, which can be solved exactly numerically with the help of a combinatorial optimization algorithm. The community structure is then identified from the ground state Ising spin domains for all pairs of $s$ and $t$. Our method provides a criterion for the existence of the community structure, and is applicable to unweighted and weighted networks equally well. We demonstrate the performance of the method by applying it to the Barab\'asi-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network.