Sharp estimates for the personalized Multiplex PageRank

PageRank can be understood as the stationary distribution of a Markov chain that occurs in a two-layer network with the same set of nodes in both layers: the physical layer and the teleportation layer. In this paper we present some bounds for the extension of this two-layer approach to Multiplex networks, establishing sharp estimates for this Multiplex PageRank and locating the possible values of the personalized PageRank for each node of a network. Several examples are shown to compare the values obtained for both algorithms, the classic and the two-layer PageRank.