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Eigenvector Localization As A Tool To Study Small Communities In Online Social Networks

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  • FRANTIŠEK SLANINA

    (Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Praha, Czech Republic)

  • ZDENĚK KONOPÁSEK

    (Center for Theoretical Study, Charles University in Prague, Academy of Sciences of the Czech Republic, Jilská 1, Praha, Czech Republic)

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.

Suggested Citation

  • František Slanina & Zdeněk Konopásek, 2010. "Eigenvector Localization As A Tool To Study Small Communities In Online Social Networks," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 699-723.
    • Handle: RePEc:wsi:acsxxx:v:13:y:2010:i:06:n:s0219525910002840
    DOI: 10.1142/S0219525910002840
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    References listed on IDEAS

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    Cited by:

    1. Frantisek Slanina, 2014. "Complex temporal structure of activity in on-line electronic auctions," Papers 1401.2860, arXiv.org.

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