Topological structure and the H-index in complex networks

TL;DR

This paper analyzes the generalized Hirsch index in complex networks, providing analytical insights, validating with simulations, and comparing its effectiveness for identifying influential nodes.

Contribution

It offers a detailed analytical characterization of the generalized H-index, connecting it to degree and validating its use in real and synthetic networks.

Findings

H(n) interpolates between degree and K-core centrality

H(n) correlates with degree in networks

Non-Backtracking centrality outperforms H-index in identifying influential spreaders

Abstract

The generalized $H(n)$ Hirsch index of order $n$ has been recently introduced and shown to interpolate between the degree and the $K$-core centrality in networks. We provide a detailed analytical characterization of the properties of sets of nodes having the same $H(n)$, within the annealed network approximation. The connection between the Hirsch indices and the degree is highlighted. Numerical tests in synthetic uncorrelated networks and real-world correlated ones validate the findings. We also test the use of the Hirsch index for the identification of influential spreaders in networks, finding that it is in general outperformed by the recently introduced Non-Backtracking centrality.