Lauritzen, Steffen; Rinaldo, Alessandro; Sadeghi, Kayvan On exchangeability in network models. (English) Zbl 1418.60028 J. Algebr. Stat. 10, No. 1, Spec. Iss., 85-114 (2019). Summary: We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their implications, between statistical network models that are finitely exchangeable and models that define a consistent sequence of probability distributions on graphs of increasing size. Cited in 5 Documents MSC: 60G09 Exchangeability for stochastic processes 05C80 Random graphs (graph-theoretic aspects) 62H99 Multivariate analysis Keywords:de Finetti’s theorem; graphons; Möbius simplex; finite exchangeability; positive semidefinite functions PDFBibTeX XMLCite \textit{S. Lauritzen} et al., J. Algebr. Stat. 10, No. 1, 85--114 (2019; Zbl 1418.60028) Full Text: DOI arXiv Online Encyclopedia of Integer Sequences: Number of graphs on n unlabeled nodes. Number of connected graphs with n nodes.