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

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

2011-05-25

arxiv.org/abs/1105.5053v1

Advances in Complex Systems 13 (2010) 699-723

Physics

Physics and Society

Scientific paper

10.1142/S0219525910002840

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.

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