Quantifying structure in networks

Details Quantifying structure in networks Quantifying structure in networks

2009-12-22

arxiv.org/abs/0912.4450v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

17 pages, 3 figures

Scientific paper

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.

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