Talk by Ernesto Estrada
On February 17th, 2021, Prof. Dr. Ernesto Estrada (University of Zaragoza) gave a talk about "Hubs-biased Laplacian operators and hubs-biased dynamics on graphs/networks" as part of the research seminar Analysis of the FernUniversität in Hagen.
I will start by motivating the topic by considering some dynamical processes on a graph, such as diffusive and synchronization ones. Then, I will introduce the notion of degree-biased dynamics and will motivate it with examples. At this point I will introduce the hubs-biased Laplacian operators for graphs and will present some of their properties, mainly spectral ones. I will use these operators in hubs-biased diffusion and synchronization on networks, such as in activation in brain networks, propagation flight delays in airports and sync of autonomous robots. Finally, I will introduce and briefly study the hubs-biased resistance metrics on graphs. I will dedicate a couple of slides to mention some future directions of this topic.
Estrada E. ‘Hubs-repelling’ Laplacian and related diffusion on graphs/networks. Linear Algebra and its Applications, 2020 596, 256-280.
Gambuzza LV, Frasca M, Estrada E. Hubs-attracting Laplacian and Related Synchronization on Networks. SIAM Journal on Applied Dynamical Systems. 2020, 19, 1057-79.