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The H-index of a network node and its relation to degree and coreness

Author

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  • Linyuan Lü

    (Alibaba Research Center for Complexity Sciences, Alibaba Business College, Hangzhou Normal University)

  • Tao Zhou

    (CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China
    Big Data Research Center, Univesrsity of Electronic Science and Technology of China)

  • Qian-Ming Zhang

    (CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China
    Boston University)

  • H. Eugene Stanley

    (Alibaba Research Center for Complexity Sciences, Alibaba Business College, Hangzhou Normal University
    Boston University)

Abstract

Identifying influential nodes in dynamical processes is crucial in understanding network structure and function. Degree, H-index and coreness are widely used metrics, but previously treated as unrelated. Here we show their relation by constructing an operator , in terms of which degree, H-index and coreness are the initial, intermediate and steady states of the sequences, respectively. We obtain a family of H-indices that can be used to measure a node’s importance. We also prove that the convergence to coreness can be guaranteed even under an asynchronous updating process, allowing a decentralized local method of calculating a node’s coreness in large-scale evolving networks. Numerical analyses of the susceptible-infected-removed spreading dynamics on disparate real networks suggest that the H-index is a good tradeoff that in many cases can better quantify node influence than either degree or coreness.

Suggested Citation

  • Linyuan Lü & Tao Zhou & Qian-Ming Zhang & H. Eugene Stanley, 2016. "The H-index of a network node and its relation to degree and coreness," Nature Communications, Nature, vol. 7(1), pages 1-7, April.
    • Handle: RePEc:nat:natcom:v:7:y:2016:i:1:d:10.1038_ncomms10168
    DOI: 10.1038/ncomms10168
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