Speaker: Prof. Norbert Peyerimhoff, Durham University
Title: How to measure the connectivity of a network?
Abstract: Networks become increasingly important in modern times and it is natural to investigate their connectivity properties. The mathematical description of a network is a graph with its vertices and edges. In this talk, I will discuss various ways to measure the connectivity of a graph with particular emphasis on the global edge expansion constant and a local graph curvature notion. The edge expansion constant, also called Cheeger isoperimetric constant, is used in the definition of expander graph families, which are families of sparse graphs with good connectivity properties. The curvature notion, based on Optimal Tranportation, is due to Yann Ollivier who is a mathematician by training but now works as a research scientist at Facebook. A challenging problem is to understand relations between these various connectivity notions. I hope to address this issue in the talk as well.