Applied Mathematics Seminar | Guanrong (Ron) Chen, Searching for Undirected Networks with Best Synchronizability

The synchronizability of a connected undirected network is essentially determined by the spectrum of its Laplacian matrix, which reflects most topological characteristics of the underlying network such as degree distribution, shortest-path length, betweenness centrality, among others. Recently, through spectral analysis, we found that networks with best synchronizability are in some sense “homogenous” and “symmetrical”, with several common features such as a near-identical degree sequence, a longest girth, and a shortest path-sum. We have verified this observation by degree-3 regular networks of small sizes, and we conjecture that it is true in general. In this talk, we will introduce the network model, define the mathematical problem, provide the necessary background information, discuss the relevant spectral analysis, and demonstrate the interesting findings and theoretical results.

Speaker’s Bio: Prof Chen received the MS degree in Computational Mathematics from Sun Yat-sen University, China in 1981 and the PhD degree in Applied Mathematics from Texas A&M University, USA in 1987. He is a Fellow of the IEEE (1997) and a Member of the Academia Europaea (2014).