A Perron–Frobenius theory for block matrices associated to a multiplex network. (March 2015)

• Record Type: Journal Article
• Authors: Romance, Miguel; Solá, Luis; Flores, Julio; García, Esther; García del Amo, Alejandro; Criado, Regino
• Is Part Of: Chaos, solitons and fractals. Volume 72(2015)
• Page Start: 77
• Page End: 89
• Publication Date: 2015-03
• Subjects: Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2014.12.020
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a multiplex network and the irreducibility of the corresponding matrices to each layer as well as the irreducibility of the adjacency matrix of the projection network. In addition the computation of that Perron vector in terms of the Perron vectors of the blocks is also addressed. Finally we present the precise relations that allow to express the Perron eigenvector of the multiplex network in terms of the Perron eigenvectors of its layers.