Mutual or Unrequited Love: Identifying Stable Clusters in Social Networks with Uni- and Bi-directional Links

TL;DR

This paper introduces a spectral clustering method that leverages mutuality tendencies in directed social networks to identify more stable and meaningful community structures, outperforming traditional methods.

Contribution

It develops a generalized mutuality tendency theory and a spectral clustering algorithm that incorporates these tendencies for better community detection in directed social networks.

Findings

The proposed algorithm outperforms traditional spectral clustering in stability.

It effectively captures stable social communities in real datasets.

Synthetic experiments confirm the robustness of the method.

Abstract

Many social networks, e.g., Slashdot and Twitter, can be represented as directed graphs (digraphs) with two types of links between entities: mutual (bi-directional) and one-way (uni-directional) connections. Social science theories reveal that mutual connections are more stable than one-way connections, and one-way connections exhibit various tendencies to become mutual connections. It is therefore important to take such tendencies into account when performing clustering of social networks with both mutual and one-way connections. In this paper, we utilize the dyadic methods to analyze social networks, and develop a generalized mutuality tendency theory to capture the tendencies of those node pairs which tend to establish mutual connections more frequently than those occur by chance. Using these results, we develop a mutuality-tendency-aware spectral clustering algorithm to identify more stable clusters by maximizing the within-cluster mutuality tendency and minimizing the cross-cluster mutuality tendency. Extensive simulation results on synthetic datasets as well as real online social network datasets such as Slashdot, demonstrate that our proposed mutuality-tendency-aware spectral clustering algorithm extracts more stable social community structures than traditional spectral clustering methods.