## Ernesto Estrada

"The Geometry of Communication in Networks"**Abstract**

I will start by motivating and defining the concept of network communicability. I then will illustrate some of the paradoxes that arise when the 'information' is assumed to flow through the shortest paths in real-world complex networks. This will follow by the introduction of a function that accounts for the goodness of communication among a pair of nodes in the network. I will prove that this corresponds to an Euclidean distance between the corresponding nodes. I will then introduce the concept of angles of communicability and will illustrate some of its mathematical properties. The talk will continue by proving that the communicability distances/angles induces an embedding of a network into a high-dimensional sphere (hypersphere). I will then illustrate how the communicability distance/angles can be applied to solve problems in the analysis of real-world complex networks.

**Short biography**

Ernesto Estrada is full professor and Chair in Complexity Sciences at the Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK. He has proven experience in developing and applying physico-mathematical tools for studying complex networks. Prof. Estrada has published more than 160 scientific papers, which have received more than 6,100 citations and he has an h-index of 46. He serves as the Editor-in-Chief of the Journal of Complex Networks, published by Oxford University Press (OUP). He maintains strong collaborations with applied mathematicians and physicists in several universities across the World. Prof. Estrada has been plenary speaker in several major international conferences, including the 2012 SIAM Annual Meeting. He has taught courses about complex networks at Strathclyde, AIMS (South Africa) and Emory University, where he is a Fellow of the Institute of Quantitative Theory and Methods. His book The Structure of Complex Networks, published by OUP, is a reference text in many courses at different universities. Prof. Estrada has given seminars and colloquia in many universities of Europe, Asia and America.