For the Spring, 2006 semester, the seminar will be devoted to Scale-free Networks. These networks arise in a remarkable number of areas: computer networks, such as the World Wide Web, social networks, the networks formed by spreading diseases, and areas of physics, as well as several other areas as well. As opposed to random networks, where one expects the number of edges each node has to be uniformly distributed, in scale free networks, the number of other nodes each node is connected to by an edge obeys a power law, and this implies that there are a few ''highly connected'' nodes in such a graph, while most nodes have relatively few edges. For a brief introduction and history of the area, see Wikipedia's page. A related phenomenon is the ''small world phenomenon,'' in which adding a small number of edges randomly to a given graph results in a dramatic drop in the diameter of the graph.
We are setting up a reading list below, and we intend to have ome of these papers presented in the seminar.
The first meeting will be on Friday, January 27, and Aaron Jaggard will lecture on Random Graphs. Research in this area, initiated by Erdos and Renyi, preceded the work in scale-free networks, so this will provide a good background for the area. In succeeding weeks, there will be talks based on survey papers by the leading researchers in the area -- Albert-Laszlo Barabasi, M. E. J. Newman and Duncan Watts. After that, the topics in the seminar will be dictated by the interests of the participants.
Here is a list of papers we have archive here on this topic: