Authors
Francisco Pedroche, Esther GarcĂa, Miguel Romance, Regino Criado
Journal Paper
https://doi.org/10.1016/j.cam.2018.05.033
Publisher URL
https://www.sciencedirect.com/
Publication date
December 2018
In this paper, we present some results about the spectrum of the matrix associated with the computation of the Multiplex PageRank defined by the authors in a previous paper. These results can be considered as a natural extension of the known results about the spectrum of the Google matrix. In particular, we show that the eigenvalues of the transition matrix associated with the multiplex network can be deduced from the eigenvalues of a block matrix containing the stochastic matrices defined for each layer. We also show that, as occurs in the classic PageRank, the spectrum is not affected by the personalization vectors defined on each layer but depends on the parameter that controls the teleportation. We also give some analytical relations between the eigenvalues and we include some small examples illustrating the main results.