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MiS Preprint
81/2009
Quantifying structure in networks
Eckehard Olbrich, Thomas Kahle, Nils Bertschinger, Nihat Ay and Jürgen Jost
Abstract
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.
