Community detection in network using Szegedy quantum walk

TL;DR

This paper introduces a quantum walk-based method using Szegedy's quantum walk to detect communities in networks, leveraging quantum properties to improve community identification in complex graphs.

Contribution

It develops a novel community detection procedure based on Szegedy's quantum walk, advancing quantum algorithms for network analysis.

Findings

Effective detection of communities in various network types.

Quantum walk approach provides a new perspective on community boundaries.

Method applied successfully to social and synthetic networks.

Abstract

In a network, the vertices with similar characteristics construct communities. The vertices in a community are well-connected. Detecting the communities in a network is a challenging and important problem in the theory of complex networks. One approach to solving this problem uses the classical random walks on graphs. In quantum computing, quantum walks are the quantum mechanical counterparts of classical random walks. In this article, we employ a variant of Szegedy's quantum walk to develop a procedure for discovering the communities in networks. The limiting probability distribution of quantum walks assists us in determining the inclusion of a vertex in a community. We apply our community detection procedure to a variety of graphs and social networks, including the relaxed caveman graph, $l$-partition graph, Karate club graph, and the dolphin's social network, among others.