title: Topological structure and the H index in complex networks.
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 analytic 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 nonbacktracking centrality.
authors.affiliation: Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain.
authors.forename: Romualdo
authors.initials: R
authors.lastname: Pastor-Satorras
authors.affiliation: Istituto dei Sistemi Complessi (ISC-CNR), Via dei Taurini 19, I-00185 Roma, Italy.|Dipartimento di Fisica, "Sapienza" Università di Roma, Piazzale Aldo Moro 2, I-00185 Roma, Italy.
authors.forename: Claudio
authors.initials: C
authors.lastname: Castellano