PHYSICS COLLOQUIUM

Speaker: Dr. J.-P. Eckmann, University of Geneva

Date: Wednesday, November 10, 2004

Time: 16:45 h (coffee/tea at 16:15 h in front of auditorium)

Place: ETH Hönggerberg, HPV G4

Title: The Use of Geometry and Entropy in Analyzing Large Networks

Abstract:

In the last few years, large Networks have become an object of intense study, and statistical properties of many examples have been analyzed: The Web, biological networks,... In my talk, I will summarize work which goes in a more conceptual direction, done with Elisha Moses and Danilo Sergi. Our aim is to relate "context" and "geometrical properties" in such networks. We use local structures to capture these properties: On the static level, this is the "clustering coefficient" (a ratio of triangles and links) which can be used to extract relevant information from the local geometry of large networks. On the dynamic level, we use relative entropy (Kullback-Leibler) in the time-domain to capture the creation of a dynamic network in e-mail traffic. I will try to explain the geometric ideas behind these studies and will illustrate how they are being applied and tested in a variety of networks we have studied: World wide web, Protein Networks, Citations, e-mail.