Range-dependent random graphs and their application to modeling large small-world Proteome datasets.

In this paper we consider the problem of characterizing and modeling large-scale networks using classes of range-dependent graphs which possess appropriate small-world properties. The application we have in mind is to bioinformatics, where methods of rapid protein identification mean that such proteome datasets, listing various observed protein-protein associations, will become more and more prevalent. We introduce a class of range-dependent graphs, governed by a power law relating intervertex range to edge probability, which are amenable to analysis, and for which macroscopic graph parameters are given by explicit forms. We show how these may be employed in representing a given network using a maximum likelihood approach. This in turn annotates every given edge with its range, representing the tendency for such an association to be transitive. We apply this technique to published proteome data, and demonstrate that known protein associations are thus identified.