Statistical null models for biological network analysis

Abstract

Statistical ensembles of random graphs serve as null models in the statistical analysis of real complex networks. They encapsulate what are believed to be the generic properties of networks and describe the expected behaviour against which observed network data can be compared. Here we review the basic statistical physics underlying statistical ensembles of networks and show how we can exploit their properties. We also show how the simple statistical ensembles that have been used to describe networks can be improved by conditioning the ensembles on other available data. We show that such conditional ensembles provide biologically more realistic network null models which can be used for more ..