title: The H-index of a network node and its relation to degree and coreness.
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.
authors.affiliation: Alibaba Research Center for Complexity Sciences, Alibaba Business College, Hangzhou Normal University, Hangzhou 311121, China.
authors.forename: Linyuan
authors.initials: L
authors.lastname: Lü
authors.affiliation: CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China.|Big Data Research Center, Univesrsity of Electronic Science and Technology of China, Chengdu 611731, China.
authors.forename: Tao
authors.initials: T
authors.lastname: Zhou
authors.affiliation: CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China.|Department of Physics and Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Qian-Ming
authors.identifier: http://orcid.org/0000-0002-1380-2438
authors.initials: QM
authors.lastname: Zhang
authors.affiliation: Alibaba Research Center for Complexity Sciences, Alibaba Business College, Hangzhou Normal University, Hangzhou 311121, China.|Department of Physics and Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: H Eugene
authors.initials: HE
authors.lastname: Stanley