  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.
