................................................................................................................................................. 3 Acknowledgements................................................................................................................................ 6 List of Tables...........................................................................................

Graphical Markov models use graphs ei ther undirected directed or mixed to rep resent possible dependences among statis tical variables Applications of undirected graphs UDGs include models for spatial de pendence and image analysis while acyclic directed graphs ADGs which are espe cially convenient for statistical analysis arise in such elds as genetics and psychomet rics and as models for exp...

Bayesian networks are a popular representation of asymmetric (for example causal) relationships between random variables. Markov random fields (MRFs) are a complementary model of symmetric relationships used in computer vision, spatial modeling, and social and gene expression networks. A chain graph model under the Lauritzen-Wermuth-Frydenberg interpretation (hereafter a chain graph model) gene...

The switch chain is a well-known Markov chain for sampling directed graphs with a given degree sequence. While not ergodic in general, we show that it is ergodic for regular degree sequences. We then prove that the switch chain is rapidly mixing for regular directed graphs of degree d, where d is any positive integer-valued function of the number of vertices. We bound the mixing time by boundin...

We consider the problem of generating a random q-colouring of a graph G = (V, E). We consider the simple Glauber Dynamics chain. We show that if for all v ∈ V the average degree of the subgraph Hv induced by the neighbours of v ∈ V is ∆ where ∆ is the maximum degree and ∆ > c1 ln n then for sufficiently large c1, this chain mixes rapidly provided q/∆ > α, where α ≈ 1.763 is the root of α = e. F...

We give the first linear-time certifying algorithms to recognize split graphs, threshold graphs, bipartite chain graphs, cobipartite chain graphs and trivially perfect graphs, with sublinear certificates for negative output. In case of membership in a given graph class our algorithms provide as certificate a structure for the input graph that characterizes the class, and in case of non-membersh...

We give the first linear-time certifying algorithms to recognize split graphs, threshold graphs, chain graphs, co-chain graphs and trivially perfect graphs, with sublinear certificates for negative output. In case of membership in a given graph class our algorithms provide as certificate a structure for the input graph that characterizes the class, and in case of non-membership they provide as ...

let $n$ be any positive integer and let $f_n$ be the friendship (or dutch windmill) graph with $2n+1$ vertices and $3n$ edges. here we study graphs with the same adjacency spectrum as the $f_n$. two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. let $g$ be a graph cospectral with $f_n$. here we prove that if $g$ has no cycle of length $4$ or $...

In this paper we study how different theoretical concepts of Bayesian networks have been extended to chain graphs. Today there exist mainly three different interpretations of chain graphs in the literature. These are the Lauritzen-Wermuth-Frydenberg, the Andersson-Madigan-Perlman and the multivariate regression interpretations. The different chain graph interpretations have been studied indepen...