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 -'?, localization occurs on the largest hub if ? > 5/2; for ? < 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.
Distinct types of eigenvector localization in networks
Claudio Castellano
2016
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 -'?, localization occurs on the largest hub if ? > 5/2; for ? < 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.File | Dimensione | Formato | |
---|---|---|---|
prod_347391-doc_109302.pdf
accesso aperto
Descrizione: Distinct types of eigenvector localization in networks
Tipologia:
Versione Editoriale (PDF)
Licenza:
Creative commons
Dimensione
1.43 MB
Formato
Adobe PDF
|
1.43 MB | Adobe PDF | Visualizza/Apri |
prod_347391-doc_109303.pdf
accesso aperto
Descrizione: Suppl_material
Tipologia:
Versione Editoriale (PDF)
Licenza:
Creative commons
Dimensione
1.52 MB
Formato
Adobe PDF
|
1.52 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.