Exact Rank-Reduction of Network Models
January 29th, 2020 ÀLEX ARENAS Universitat Rovira i Vigili

With the advent of the big data era, models of complex networks are becoming elusive from direct computational simulation. We present an exact, linear-algebraic reduction scheme of undirected network models. We group them in universality classes, and work out, in a computationally aordable way, their relevant properties (e.g., spectrum). By exploiting the bilinearity structure of the expected adjacency matrix of the network, we separate its null eigenspace, and reduce the exact description of the model to a smaller vector space. We show that the rank and signature of such matrix entail a natural and comprehensive classication of network models. The reduction also provides the environment for a simplied computation of their properties. The proposed scheme will be very useful in the study of dynamical processes on networks, as well as in the understanding of models to come, according to the provided universal classification.

Seminar, January 29, 2020, 16:00. ICFO’s Seminar Room

Hosted by Prof. Antonio Acín