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

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…

• NS
  National Science Foundation

  Awards: 1505000, 1213217, 1125290, CHE 1213217, PHY 1505000
• NN
  National Natural Science Foundation of China

  Awards: 611272, 11222543, 11205042, 11075031, 61433014
• HN
  Hangzhou Normal University

  Award: PE13002004039
• DO
  Division of Civil, Mechanical and Manufacturing Innovation

  Awards: 1125290, CMMI 1125290
• DO
  Division of Chemistry

  Award: 1213217