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.