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

Linyuan Lü (), Tao Zhou, Qian-Ming Zhang and H. Eugene Stanley ()
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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
Qian-Ming Zhang: CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China
H. Eugene Stanley: Alibaba Research Center for Complexity Sciences, Alibaba Business College, Hangzhou Normal University

Nature Communications, 2016, vol. 7, issue 1, 1-7

Abstract: 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.

Date: 2016
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DOI: 10.1038/ncomms10168

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