The harmonic influence is a measure of node influence in social networks that quantifies the ability of a leader node to alter the average opinion of the network, acting against an adversary field node. The definition of harmonic influence assumes linear interactions between the nodes described by an undirected weighted graph; its computation requires to solve, for every node, a discrete Dirichlet problem associated to a grounded Laplacian. In this talk, I will describe a message-passing distributed algorithm that concurrently computes the harmonic influence of all nodes and provide a convergence analysis for it. The algorithm converges asymptotically, under the only assumption of the interaction Laplacian being symmetric. However, the convergence value does not in general coincide with the harmonic influence: simulations show that when the network has a larger number of cycles, the algorithm becomes slower and less accurate, but nevertheless provides a useful approximation. Simulations also indicate that the symmetry condition is not necessary for convergence and that performance (both in terms of speed and asymptotical error) scales well in the number of nodes of the graph.

Bio. Paolo Frasca received the Ph.D. degree in Mathematics for Engineering Sciences from Politecnico di Torino, Torino, Italy, in 2009. Between 2008 and 2013, he has held research and visiting positions at the University of California, Santa Barbara (USA), at the IAC-CNR (Rome, Italy), at the University of Salerno (Italy), and at the Politecnico di Torino. From 2013 to 2016, he has been an Assistant Professor at the University of Twente in Enschede, the Netherlands. In October 2016 he joined the CNRS as Researcher: he is currently affiliated with GIPSA-lab in Grenoble, France.

His research interests are in the theory of network systems and cyber-physical systems, with applications to robotic, sensor, infrastructural, and social networks. On these topics, Dr. Frasca has (co)authored more than fifty journal and conference papers and has given invited talks at several international institutions and events, including the 2015 SICE International Symposium on Control Systems in Tokyo. He is a recipient of the 2013 SIAG/CST Best SICON Paper Prize. He has been a visiting professor at the LAAS, Toulouse, France in 2016 and at the University of Cagliari, Italy in 2017.

Dr. Frasca has served as Associate Editor of several international conferences, including IEEE CDC, ACC, ECC, MTNS, IFAC NecSys, and is currently serving as Associate Editor for the International Journal of Robust and Nonlinear Control, the Asian Journal of Control, and the IEEE Control Systems Letters.