Seminario Rubio de Francia: “Hubs-biased Laplacians on graphs/networks”.-Jueves 18 de febrero

Última modificación: 10/02/2021 - 10:55

Jueves, Febrero 18, 2021

El jueves 18 de febrero a las 12.00 h tendrá lugar la conferencia de este ciclo que la impartirá Ernesto Estrada (IUMA-Universidad de Zaragoza). Se titula "Hubs-biased Laplacians on graphs/networks", y podréis seguirla online desde zoom:


Laplacian operators are ubiquitous in graphs. In finite graphs, the standard Laplacian matrix is defined on the basis of the adjacency matrix of the graph. It is widely used in most dynamical systems on graphs/networks, such as diffusion/consensus and synchronization processes. Accordingly, a particle located at a given node can hop to any of its nearest neighbors with equal probability. That is, the hoping probability depends only on the number of connections (degree) of the node on which the particle resides at time t, and not on the degree of those nodes that the particle will visit at time t+1. Here I extend the notion of graph Laplacian to account for processes in which the hopping probability of a particle at a given node depends not only on the degree of this node but also on the degree of its nearest neighbors. Therefore, I introduce two classes of Laplacians, hubs-repelling and hubs-attracting ones, which accounts for different ways in which nodes affect the dynamic on the graph. Namely, they can repel/attract the particle in different ways proportional to their degrees. I will study several properties of these hubs-biased Laplacians, mainly spectral ones, and relate them to hubs-biased diffusion processes and synchronization of oscillators.