An Eigenvector Centrality for Multiplex Networks with Data

Networks are useful to describe the structure of many complex systems. Often, understanding these systems implies the analysis of multiple interconnected networks simultaneously, since the system may be modelled by more than one type of interaction. Multiplex networks are structures capable of describing networks in which the same nodes have different links. Characterizing the centrality of nodes in multiplex networks is a fundamental task in network theory. In this paper, we design and discuss a centrality measure for multiplex networks with data, extending the concept of eigenvector centrality. The essential feature that distinguishes this measure is that it calculates the centrality in multiplex networks where the layers show different relationships between nodes and where each layer has a dataset associated with the nodes. The proposed model is based on an eigenvector centrality for networks with data, which is adapted according to the idea behind the two-layer approach PageRank. The core of the centrality proposed is the construction of an irreducible, non-negative and primitive matrix, whose dominant eigenpair provides a node classification. Several examples show the characteristics and possibilities of the new centrality illustrating some applications.