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Distinct types of eigenvector localization in networks

Scientific reports, 2016-01, Vol.6 (1), p.18847-18847, Article 18847 [Peer Reviewed Journal]

Copyright Nature Publishing Group Jan 2016 ;info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/3.0/es/ ;Copyright © 2016, Macmillan Publishers Limited 2016 Macmillan Publishers Limited ;ISSN: 2045-2322 ;EISSN: 2045-2322 ;DOI: 10.1038/srep18847 ;PMID: 26754565

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  • Title:
    Distinct types of eigenvector localization in networks
  • Author: Pastor-Satorras, Romualdo ; Castellano, Claudio
  • Subjects: Anàlisi numèrica ; Complex networks ; Eigenvectors ; Física ; Localization ; Matemàtiques i estadística ; Nets (Mathematics) ; Nodes ; Statistical physics ; Structure-function relationships ; Vector propis ; Xarxes (Matemàtica) ; Àrees temàtiques de la UPC
  • Is Part Of: Scientific reports, 2016-01, Vol.6 (1), p.18847-18847, Article 18847
  • Description: 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.
  • Publisher: England: Nature Publishing Group
  • Language: English
  • Identifier: ISSN: 2045-2322
    EISSN: 2045-2322
    DOI: 10.1038/srep18847
    PMID: 26754565
  • Source: Recercat
    PubMed Central
    ProQuest Central
    DOAJ Directory of Open Access Journals
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