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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Received:
Dec 22, 2009
Published:
Dec 23, 2009
MSC Codes:
05C80
PACS:
89.75.Hc

Related publications

inJournal
2010 Repository Open Access
Eckehard Olbrich, Thomas Kahle, Nils Bertschinger, Nihat Ay and Jürgen Jost

Quantifying structure in networks

In: The European physical journal / B, 77 (2010) 2, pp. 239-247