Role extraction by matrix equations and generalized random walks

TL;DR

This paper introduces a novel similarity matrix for directed networks, utilizing matrix equations and generalized random walks to improve role extraction based on connection patterns.

Contribution

It proposes a new similarity measure defined via matrix equations that accounts for link directions and random walks, enhancing role detection in directed networks.

Findings

Performs well on directed networks with heterogeneous degrees

Outperforms existing role extraction methods

Effective in capturing node similarity based on connection patterns

Abstract

The nodes in a network can be grouped into 'roles' based on similar connection patterns. This is usually achieved by defining a pairwise node similarity matrix and then clustering rows and columns of this matrix. This paper presents a new similarity matrix for solving role extraction problems in directed networks, which is defined as the solution of a matrix equation and computes node similarities based on random walks that can proceed along the link direction and in the opposite direction. The resulting node similarity measure performs remarkably in role extraction tasks on directed networks with heterogeneous node degree distributions.