Node and layer eigenvector centralities for multiplex networks

Abstract

Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extremely simple in the framework of standard, mono-layer networks. Moreover, several efficient computational tools are available for their computation. Moving up in dimensionality, several efforts have been made in the past to describe an eigenvector-based centrality measure that generalizes Bonacich index to the case of multiplex networks. In this work, we propose a new definition of eigenvector centrality that relies on the Perron eigenvector of a multi-homogeneous map defined in terms of the tensor describing the network. We prove that existence and uniqueness of such centrality are guaranteed under very mild assumptions on the multiplex network. Extensive numerical studies are proposed to test the newly introduced centrality measure and to compare it to other existing eigenvector-based centralities.

author's accepted version

References in corpus (17)

• Finding community structure in networks using the eigenvectors of matrices
• Multilayer Networks
• The structure and dynamics of multilayer networks
• Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
• Structural measures for multiplex networks
• Random Walks on Multiplex Networks
• Emergence of network features from multiplexity
• Centrality in Interconnected Multilayer Networks
• Narrow scope for resolution-limit-free community detection
• Statistical Mechanics of Multiplex Ensembles: Entropy and Overlap
• Eigenvector centrality of nodes in multiplex networks
• Growing multiplex networks
• Prediction and Clustering in Signed Networks: A Local to Global Perspective
• The Perron-Frobenius theorem for multi-homogeneous mappings
• Clustering Signed Networks with the Geometric Mean of Laplacians
• An algebraic analysis of the graph modularity
• The Perron-Frobenius Theorem for Multi-homogeneous Maps

Cited by in corpus (10)

• The Perron-Frobenius theorem for multi-homogeneous mappings
• A unifying Perron-Frobenius theorem for nonnegative tensors via multi-homogeneous maps
• Fast computation of matrix function-based centrality measures for layer-coupled multiplex networks
• A framework for second order eigenvector centralities and clustering coefficients
• Orientations and matrix function-based centralities in multiplex network analysis of urban public transport
• The contractivity of cone-preserving multilinear mappings
• Perron communicability and sensitivity of multilayer networks
• Bias-Variance Tradeoffs in Joint Spectral Embeddings
• Quantifying the structural stability of simplicial homology
• Eigenvector centrality for multilayer networks with dependent node importance