Strong and Weak Random Walks on Signed Networks

TL;DR

This paper introduces a novel random walk method for signed networks that effectively captures multiple community structures, outperforming traditional approaches in clustering tasks on complex, real-world signed networks.

Contribution

It proposes a weak balance random walk for signed networks that generalizes beyond two communities, enhancing community detection in complex signed networks.

Findings

Weak walks outperform strong walks in multi-community detection

Similarity matrices from weak walks improve clustering accuracy

Weak walks are effective on both synthetic and real-world networks

Abstract

Random walks play an important role in probing the structure of complex networks. On traditional networks, they can be used to extract community structure, understand node centrality, perform link prediction, or capture the similarity between nodes. On signed networks, where the edge weights can be either positive or negative, it is non-trivial to design a random walk which can be used to extract information about the signed structure of the network, in particular the ability to partition the graph into communities with positive edges inside and negative edges in between. Prior works on signed network random walks focus on the case where there are only two such communities (strong balance), which is rarely the case in empirical networks. In this paper, we propose a signed network random walk which can capture the structure of a network with more than two such communities (weak balance). The walk results in a similarity matrix which can be used to cluster the nodes into antagonistic communities. We compare the characteristics of the so-called strong and weak random walks, in terms of walk length and stationarity. We show through a series of experiments on synthetic and empirical networks that the similarity matrix based on weak walks can be used for both unsupervised and semi-supervised clustering, outperforming the same similarity matrix based on strong walks when the graph has more than two communities, or exhibits asymmetry in the density of links. These results suggest that other random-walk based algorithms for signed networks could be improved simply by running them with weak walks instead of strong walks.