Title: The geometry of communication on networks
Monday, October 17 at 2pm, in Room A2002
Speaker: Prof. Ernesto Estrada (University of Strathclyde Glasgow):
DescriptionThe geometry of communication on networks I will start by considering that the communication between pairs of nodes in a network takes place uniquely via the shortest-paths connecting them. Then, I will give a few evidences against this hypothesis and will conduct the reasoning to the necessity of considering all-walks communication in networks. This immediately motivates the concept of network communicability, and I will show some examples of its applications in different fields. I will propose two quantities that account for the difference or ratio of the amount of information transmitted between two nodes and the amount of information returned to its originator. I will prove that these quantities represent a Euclidean distance between the nodes and the angle spanned by the position vectors of the corresponding nodes, respectively. I will prove that these quantities induce an embedding of any network into a Euclidean hyper-sphere. Finally, I will illustrate some potential applications of these geometric parameters of a network in different areas.