Seminar Details
2021-11-09 (14h) : Graphons for the Estimation of Performance Indices in Large Networks
At Euler building (room a.002)
Organized by Mathematical Engineering
Speaker :
Renato Vizuete (CentraleSupélec and GIPSA-lab, France )
Abstract :
In recent years, the analysis of large networks has received increasing attention in many scientific fields due to the continuous evolution of the world towards a networked environment with a large number of connections. In this type of networks, uncertainties are almost present, and even the graph topology may not be available, which makes the analysis more complicated. One of the most promising tools to address these problems are graphons, defined as the limits of convergent sequences of dense graphs. In this talk, we will present the fundamentals of graphons and their applications in the estimation of performance indices associated with large networks sampled from graphons. In the first part, we will analyze the stability of a SIS epidemic over a network and its robustness to noise using the properties of the graphon operator. For the second application, we will present a study of the spectrum of the Laplacian matrix of a graph using the degree function of the graphon and the estimation of the well known average effective resistance of sampled networks.