Multi-Dimensional, Multilayer, Nonlinear and Dynamic HITS

TL;DR

This paper proposes a nonlinear, multi-dimensional extension of the HITS algorithm for dynamic, multilayer networks, ensuring unique centrality measures and providing an efficient computation method validated on real data.

Contribution

It introduces a novel nonlinear ranking model for temporal multilayer networks based on a Perron eigenvector approach, guaranteeing existence, uniqueness, and computational efficiency.

Findings

Model effectively captures multi-dimensional, temporal network centralities

Algorithm converges globally and efficiently computes centrality vectors

Numerical experiments demonstrate the model's practical effectiveness

Abstract

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 one for the temporal stamps. Nonlinearity is introduced in the standard HITS model in order to guarantee existence and uniqueness of these centrality vectors for any network, without any requirement on its connectivity structure. We introduce a globally convergent power iteration like algorithm for the computation of the centrality vectors. Numerical experiments on real-world networks are performed in order to assess the effectiveness of the proposed model and showcase the performance of the accompanying algorithm.