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Rich-Cores in Networks

Author

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  • Athen Ma
  • Raúl J Mondragón

Abstract

A core comprises of a group of central and densely connected nodes which governs the overall behaviour of a network. It is recognised as one of the key meso-scale structures in complex networks. Profiling this meso-scale structure currently relies on a limited number of methods which are often complex and parameter dependent or require a null model. As a result, scalability issues are likely to arise when dealing with very large networks together with the need for subjective adjustment of parameters. The notion of a rich-club describes nodes which are essentially the hub of a network, as they play a dominating role in structural and functional properties. The definition of a rich-club naturally emphasises high degree nodes and divides a network into two subgroups. Here, we develop a method to characterise a rich-core in networks by theoretically coupling the underlying principle of a rich-club with the escape time of a random walker. The method is fast, scalable to large networks and completely parameter free. In particular, we show that the evolution of the core in World Trade and C. elegans networks correspond to responses to historical events and key stages in their physical development, respectively.

Suggested Citation

  • Athen Ma & Raúl J Mondragón, 2015. "Rich-Cores in Networks," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-13, March.
  • Handle: RePEc:plo:pone00:0119678
    DOI: 10.1371/journal.pone.0119678
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    References listed on IDEAS

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    1. V. Zlatic & G. Bianconi & A. Díaz-Guilera & D. Garlaschelli & F. Rao & G. Caldarelli, 2009. "On the rich-club effect in dense and weighted networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 67(3), pages 271-275, February.
    2. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
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    Cited by:

    1. Yang, Shuhui & Li, Zhongkai & Zhou, Jianlin & Gao, Yancheng & Cui, Xuefeng, 2024. "Evolving patterns of agricultural production space in China: A network-based approach," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 5(1), pages 121-134.
    2. Yao, Dongmin & Sun, Rong & Gao, Qiunan, 2022. "The network structure of the China bond market: Characteristics and explanations from trading factors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    3. Shen, Xin & Han, Yue & Li, Wenqian & Wong, Ka-Chun & Peng, Chengbin, 2021. "Finding core–periphery structures in large networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    4. Cinelli, Matteo & Ferraro, Giovanna & Iovanella, Antonio, 2018. "Rich-club ordering and the dyadic effect: Two interrelated phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 808-818.

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