Eigenvector localization as a tool to study small communities in online social networks

TL;DR

This paper introduces a spectral analysis method using eigenvector localization to identify small communities within large bipartite networks, demonstrated on Amazon product review data.

Contribution

The paper presents a novel eigenvector localization technique for detecting small communities in bipartite networks, complementing existing community detection methods.

Findings

Identified hybrid communities of reviewers and products on Amazon.

Eigenvector localization reveals small, densely interconnected segments.

Method provides meaningful interpretation of community structure.

Abstract

We present and discuss a mathematical procedure for identification of small "communities" or segments within large bipartite networks. The procedure is based on spectral analysis of the matrix encoding network structure. The principal tool here is localization of eigenvectors of the matrix, by means of which the relevant network segments become visible. We exemplified our approach by analyzing the data related to product reviewing on Amazon.com. We found several segments, a kind of hybrid communities of densely interlinked reviewers and products, which we were able to meaningfully interpret in terms of the type and thematic categorization of reviewed items. The method provides a complementary approach to other ways of community detection, typically aiming at identification of large network modules.