### DIMACS Computational and Mathematical Epidemiology Seminar Series

Title: Spreading Dynamics on Small-World Networks with a Power Law Degree Distribution

Speaker: **Alexei Vazquez**, Institute for Advanced Study

Date: December 4, 2006 12:00 - 1:30 pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

I study the spreading dynamics on small world networks with a power law
degree distribution. I demonstrate that when the second moment of the
degree distribution diverges with increasing the graph size there is a
qualitative change in the growth pattern, deviating from the standard
exponential growth. First, the spreading dynamics is extensive, meaning
that the average number of vertices reached by the spreading process
becomes of the order of the graph size in a time scale that vanishes in
the large graph size limit. Second, the temporal evolution is governed by
a polynomial growth, with a degree determined by the characteristic
distance between vertices in the graph.

see: DIMACS
Computational and Mathematical Epidemiology Seminar Series 2006 -
2007