Fast Computation of Eigenvector Centralities for Multilayer Networks with Nonnegative Tensor Train
Lobachevskii Journal of Mathematics, vol. 46, pp. 3804–3814, 2025
In this article, we introduce eigenvector centralities for higher-order multilayer networks and suggest to use nonnegative tensor train decomposition for fast computations of dominant eigenvectors of multi-homogeneous maps via power iterates. The analysis of the approximation error for using nonnegative tensor train …
Generalized Friendship Paradoxes in Network Science
SIAM Journal on Matrix Analysis and Applications, 2026
Generalized friendship paradoxes occur when, on average, our friends have more of some attribute than us. These paradoxes are relevant to many aspects of human interaction, notably in social science and epidemiology. Here, we derive new theoretical results concerning the inevitability of a paradox arising, using a …
Node and Edge Eigenvector Centrality for Hypergraphs
Communications Physics, vol. 4:201, 2021
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency matrix. Recent work indicates that there are further benefits from accounting …
A framework for second order eigenvector centralities and clustering coefficients
Proceedings of the Royal Society A, vol. 476, pp. 20190724, 2020
We propose and analyse a general tensor-based framework for incorporating second order features into network measures. This approach allows us to combine traditional pairwise links with information that records whether triples of nodes are involved in wedges or triangles. Our treatment covers classical spectral methods …
Multi-Dimensional, Multilayer, Nonlinear and Dynamic HITS
SIAM International Conference on Data Mining (SDM), pp. 369–377, 2019
We introduce a ranking model for temporal multi-dimensional weighted and directed networks based on the Perron eigenvector of a multi-homogeneous order-preserving map. The model extends to the temporal multilayer setting the HITS algorithm and defines five centrality vectors: two for the nodes, two for the layers, and …
Node and layer eigenvector centralities for multiplex networks
SIAM Journal on Applied Mathematics, vol. 78, pp. 853–876, 2018
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 …
On the stability of network indices defined by means of matrix functions
SIAM Journal on Matrix Analysis and Applications, vol. 39, pp. 1521–1546, 2018
Identifying important components in a network is one of the major goals of network analysis. Popular and effective measures of importance of a node or a set of nodes are defined in terms of suitable entries of functions of matrices $f(A)$. These kinds of measures are particularly relevant as they are able to capture …