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Asymptotic Behaviour of the Number of Labelled Essential Acyclic Digraphs and Labelled Chain Graphs

Authors:	Email author" target="_blank">Bertran?Steinsky Email author

Institution:	(1) Department of Mathematics C, Graz University of Technology, Steyrergasse 30 / III, A-8010 Graz, Austria

Abstract:	We provide an asymptotic formula for the number of labelled essential DAGs a_n and show that lim_na_n/a_n=c, where a_n is the number of labelled DAGs and c13.65, which is interesting in the field of Bayesian networks. Furthermore, we present an asymptotic formula for the number of labelled chain graphs.Acknowledgment. I would like to thank Prof. Peter Grabner for his support and very helpful discussions, which where constitutive for this article. I am also thankful to the referees for their comments.This Research was supported by the Austrian Science Fund (FWF), START-Project Y96-MATFinal version received: January 28, 2004

Keywords:	Labelled essential directed acyclic graph Chain graph Asymptotic enumeration Bayesian network
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