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 …
Core-periphery detection in multilayer networks
Physical Review Letters, 2025
Multilayer networks provide a powerful framework for modeling complex systems that capture different types of interactions between the same set of entities across multiple layers. Core-periphery detection involves partitioning the nodes of a network into core nodes, which are highly connected across the network, and …
A nonlinear spectral core-periphery detection method for multiplex networks
Proceedings of the Royal Society A, 2024
Core-periphery detection aims to separate the nodes of a complex network into two subsets: a core that is densely connected to the entire network and a periphery that is densely connected to the core but sparsely connected internally. The definition of core-periphery structure in multiplex networks that record …
Laplacian-based Semi-Supervised Learning in Multilayer Hypergraphs by Coordinate Descent
EURO Journal on Computational Optimization, 2023
Graph Semi-Supervised learning is an important data analysis tool, where given a graph and a set of labeled nodes, the aim is to infer the labels to the remaining unlabeled nodes. In this paper, we start by considering an optimization-based formulation of the problem for an undirected graph, and then we extend this …
A Variance-aware Multiobjective Louvain-like Method for Community Detection in Multiplex Networks
Journal of Complex Networks, 2022
In this paper, we focus on the community detection problem in multiplex networks, i.e., networks with multiple layers having same node sets and no inter-layer connections. In particular, we look for groups of nodes that can be recognized as communities consistently across the layers. To this end, we propose a new …
Learning the right layers: a data-driven layer-aggregation strategy for semi-supervised learning on multilayer graphs
International Conference on Machine Learning (ICML), 2023
Clustering (or community detection) on multilayer graphs poses several additional complications with respect to standard graphs as different layers may be characterized by different structures and types of information. One of the major challenges is to establish the extent to which each layer contributes to the cluster …
Generalized matrix means for semisupervised learning with multilayer graphs
Advances in Neural Information Processing Systems (NeurIPS), 2019
We study the task of semi-supervised learning on multilayer graphs by taking into account both labeled and unlabeled observations together with the information encoded by each individual graph layer. We propose a regularizer based on the generalized matrix mean, which is a one-parameter family of matrix means that …
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 …
The Power Mean Laplacian for Multilayer Graph Clustering
International Conference on Artificial Intelligence and Statistics (AISTATS), vol. 84, pp. 1828–1838, 2018
Multilayer graphs encode different kind of interactions between the same set of entities. When one wants to cluster such a multilayer graph, the natural question arises how one should merge the information form different layers. We introduce in this paper a one-parameter family of matrix power means for merging the …
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 …