Eigenvector localization as a tool to study small communities in online social networks
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2011
- DOI:
- 10.48550/arXiv.1105.5053
- arXiv:
- arXiv:1105.5053
- Bibcode:
- 2011arXiv1105.5053S
- Keywords:
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- Physics - Physics and Society;
- Condensed Matter - Statistical Mechanics;
- Computer Science - Social and Information Networks
- E-Print:
- Advances in Complex Systems 13 (2010) 699-723