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

TLDR

Identifying influential nodes in dynamical processes is crucial for understanding network structure and function, yet degree, H‑index, and coreness have been treated as unrelated metrics. The study aims to demonstrate the relationship among degree, H‑index, and coreness by constructing an operator that links them as initial, intermediate, and steady states. They construct an operator that defines sequences where degree, H‑index, and coreness correspond to initial, intermediate, and steady states. The authors introduce a family of H‑indices that quantify node importance, prove convergence to coreness under asynchronous updates enabling decentralized calculation, and show through SI‑R simulations that the H‑index often outperforms degree or coreness in measuring node influence.

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 "Equation missing", 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.