Graph Signatures for Evaluating Network Models

Complex networks are finding increasing use in many scientific fields as a data representation. They are used to describe social networks, power grids, transportation networks, food webs and protein interactions in organisms, for example. A number of network models have been proposed to describe and explain the structure of these networks. In this paper we explore the problem of determining how well these models fit to the data, by using graph descriptors and signatures to define graph similarity and then using a model sampling approach to assess model similarity. We compare well known descriptors such as heat kernel based methods with some new signatures and propose a new method of constructing a global signature. We evaluate the performance of these descriptors on the problem of modelling protein-protein interaction networks.