Quantifying structure in networks
Eckehard Olbrich, Thomas Kahle, Nils Bertschinger, Nihat Ay, and Jürgen Jost
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Submission date: 22. Dec. 2009
published in: The European physical journal / B, 77 (2010) 2, p. 239-247
DOI number (of the published article): 10.1140/epjb/e2010-00209-0
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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.