Quantifying structure in networks*
Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
2 Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico, 87501, USA
Corresponding author: a firstname.lastname@example.org
Published online: 2 July 2010
We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of subgraphs with no more than k links are a sufficient statistics for the exponential families of graphs with interactions between at most k links. In this framework we investigate the dependencies between several observables commonly used to quantify structure in networks, such as the degree distribution, cluster and assortativity coefficients.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2010