A Poisson model for random multigraphs.

Abstract

Biological networks are often modeled by random graphs. A better modeling vehicle is a multigraph where each pair of nodes is connected by a Poisson number of edges. In the current model, the mean number of edges equals the product of two propensities, one for each node. In this context it is possible to construct a simple and effective algorithm for rapid maximum likelihood estimation of all propensities. Given estimated propensities, it is then possible to test statistically for functionally connected nodes that show an excess of observed edges over expected edges. The model extends readily to directed multigraphs. Here, propensities are replaced by outgoing and incoming propensities. The theory is applied to real data on neuronal connections, interacting genes in radiation hybrids, interacting proteins in a literature curated database, and letter and word pairs in seven Shaskespearean plays. All data used are fully available online from their respective sites. Source code and software is available from http://code.google.com/p/poisson-multigraph/.