Rich-club and page-club coefficients for directed graphs |
| |
Authors: | Daniel Smilkov Ljupco Kocarev |
| |
Affiliation: | a Macedonian Academy of Sciences and Arts, Skopje, Macedonia b BioCircuits Institute, University of California San Diego, La Jolla, CA, USA |
| |
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. |
| |
Keywords: | Directed networks Rich-club coefficient Page-club coefficient Real networks |
本文献已被 ScienceDirect 等数据库收录! |
|