title: Distinct types of eigenvector localization in networks.
abstract: The spectral properties of the adjacency matrix provide a trove of information about the structure and function of complex networks. In particular, the largest eigenvalue and its associated principal eigenvector are crucial in the understanding of nodes' centrality and the unfolding of dynamical processes. Here we show that two distinct types of localization of the principal eigenvector may occur in heterogeneous networks. For synthetic networks with degree distribution P(q) ~ q(-γ), localization occurs on the largest hub if γ > 5/2; for γ < 5/2 a new type of localization arises on a mesoscopic subgraph associated with the shell with the largest index in the K-core decomposition. Similar evidence for the existence of distinct localization modes is found in the analysis of real-world networks. Our results open a new perspective on dynamical processes on networks and on a recently proposed alternative measure of node centrality based on the non-backtracking matrix.
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, P.le A. Moro 2, I-00185 Roma, Italy.
authors.forename: Claudio
authors.initials: C
authors.lastname: Castellano