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

TLDR: A family of H-indices are obtained that can be used to measure a node's importance and it is proved that the convergence to coreness can be guaranteed even under an asynchronous updating process, allowing a decentralized local method of calculating a nodes' coreness in large-scale evolving networks.

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.