Uncovering Hierarchical Structure in Social Networks using Isospectral Reductions

TL;DR

This paper applies isospectral network reduction techniques to multi-mode social networks to reveal hierarchical structures and analyze their evolution, providing new insights into well-studied social networks.

Contribution

It introduces the use of isospectral reductions for hierarchical and dynamical analysis of multi-mode social networks, extending previous methods.

Findings

Uncovered hierarchical structures in the Southern Women Data Set.

Provided new insights complementing previous social network analyses.

Demonstrated the effectiveness of isospectral reductions in social network analysis.

Abstract

We employ the recently developed theory of isospectral network reductions to analyze multi-mode social networks. This procedure allows us to uncover the hierarchical structure of the networks we consider as well as the hierarchical structure of each mode of the network. Additionally, by performing a dynamical analysis of these networks we are able to analyze the evolution of their structure allowing us to find a number of other network features. We apply both of these approaches to the Southern Women Data Set, one of the most studied social networks and demonstrate that these techniques provide new information, which complements previous findings.