Numerical linear algebra meets multiplex networks

by Kai Bergermann (Scuola Normale Superiore)

Thursday 13 Nov 2025, 11:00 → 12:00 Europe/Rome

Sala Riunioni (Department of Mathematics)

Multiplex networks are used to model complex systems from myriad applications. They generalize classical complex networks by recording different types of relationships, different interactions, or changing interactions over time between the same entities in different layers. They possess natural linear algebraic representations in terms of structured matrices, which makes efficient numerical linear algebra techniques a valuable tool for their analysis.

In this talk, I will present contributions to multiplex network analysis relying on matrix function approximation and nonlinear spectral methods. I will discuss centrality measures, the solution of stiff systems of non-linear differential equations with exponential Runge--Kutta integrators, un- and semi-supervised community detection, and core-periphery detection. All presented methods have a linear runtime scaling, which allows the treatment of large-scale multiplex networks and numerical experiments for all considered problems will be presented.