An Eigenvector Centrality for Multiplex Networks with Data

Francisco Pedroche,Leandro Tortosa,José F Vicent

doi:10.3390/sym11060763

Francisco Pedroche, Leandro Tortosa + Show 1 more

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https://doi.org/10.3390/sym11060763

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Abstract

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.

Highlights

IntroductionThe identification of the most relevant nodes in complex networks has caught the attention of researchers because of its theoretical significance [1]
We present some numerical examples of the theoretical models studied in Section 2 for different types of networks and sizes. These examples allow the establishment of characteristics and properties of the centralities developed, with special emphasis on the possibilities offered by an eigenvector centrality for multiplex networks
To compare the results of centralities when applying both expressions, we distinguish between two measures of centrality, such as: CVP The eigenvector centrality for networks with data, using expression (3)

Summary

Introduction

The identification of the most relevant nodes in complex networks has caught the attention of researchers because of its theoretical significance [1]. It has been accepted that some complex systems can be integrated by multilayer networks that characterize different interactions [2,3,4]. The term multiplex network was applied to social networks and it indicated that the same person has more than one relationship [5]. Nowadays, it is a type of multilayer network in which a set of links determines a different layer [6,7]

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