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Rich-club and page-club coefficients for directed graphs

Author

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  • Smilkov, Daniel
  • Kocarev, Ljupco

Abstract

Rich-club and page-club coefficients and their null models are introduced for directed graphs. Null models allow for a quantitative discussion of the rich-club and page-club phenomena. These coefficients are computed for four directed real-world networks: Arxiv High Energy Physics paper citation network, Web network (released from Google), Citation network among US Patents, and email network from a EU research institution. The results show a high correlation between rich-club and page-club ordering. For journal paper citation network, we identify both rich-club and page-club ordering, showing that “elite” papers are cited by other “elite” papers. Google web network shows partial rich-club and page-club ordering up to some point and then a narrow declining of the corresponding normalized coefficients, indicating the lack of rich-club ordering and the lack of page-club ordering, i.e. high in-degree (PageRank) pages purposely avoid sharing links with other high in-degree (PageRank) pages. For UC patents citation network, we identify page-club and rich-club ordering providing a conclusion that “elite” patents are cited by other “elite” patents. Finally, for email communication network we show lack of both rich-club and page-club ordering. We construct an example of synthetic network showing page-club ordering and the lack of rich-club ordering.

Suggested Citation

  • Smilkov, Daniel & Kocarev, Ljupco, 2010. "Rich-club and page-club coefficients for directed graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(11), pages 2290-2299.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:11:p:2290-2299
    DOI: 10.1016/j.physa.2010.02.001
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    Citations

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    Cited by:

    1. Ying Lian & Xiaofeng Lin & Xuefan Dong & Shengjie Hou, 2022. "A Normalized Rich-Club Connectivity-Based Strategy for Keyword Selection in Social Media Analysis," Sustainability, MDPI, vol. 14(13), pages 1-19, June.
    2. Berahmand, Kamal & Bouyer, Asgarali & Samadi, Negin, 2018. "A new centrality measure based on the negative and positive effects of clustering coefficient for identifying influential spreaders in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 41-54.
    3. Liu, Jialin & Chen, Hongkan & Liu, Zhibo & Bu, Yi & Gu, Weiye, 2022. "Non-linearity between referencing behavior and citation impact: A large-scale, discipline-level analysis," Journal of Informetrics, Elsevier, vol. 16(3).

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