Modeling Self-Organizing Networks
Pawal Pralat
Department of Mathematics
West Virginia University
One of the most characteristic features of a graph corresponding to many self-organizing networks is its degree sequence, in which the fraction of vertices of degree larger than k decreases as a power of k. Since in the standard models of sparse random graphs the fraction of vertices of large degree decreases exponentially with k, a number of new probabilistic models of the web graph for which degree sequence obeys the power law have been proposed. Such models are useful for several reasons. They deepen our understanding of the generative mechanism driving the evolution of the web network. They provide insight into superficially unrelated properties observed in the web. Perhaps most importantly from the point of view of applications, they may aid in the development of the next generation of search engines. During my talk, I would like to focus on the spatial web graph model with local influence regions but others model will be discussed as well.