This paper deals with chain graphs under the Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. Moreover, we show that the extension of Meek’s conjecture to AMP chain graphs does not hold, which compromises the development of efficient and correct score+search lea...

Chain event graphs are a model family particularly suited for asymmetric causal discrete domains. This paper describes a dynamic programming algorithm for exact learning of chain event graphs from multivariate data. While the exact algorithm is slow, it allows reasonably fast approximations and provides clues for implementing more scalable heuristic algorithms.

In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random ...

For modelling diseases in medicine, chain graphs are more attractive than directed graphs, i.e., Bayesian networks, as they support representing interactions between diseases that have no natural direction. In particular, representation by chain graphs is preferred over Bayesian networks as they have the ability to capture equilibrium models. Using qualitative abstractions of probabilistic inte...

the first ($pi_1$) and the second $(pi_2$) multiplicative zagreb indices of a connected graph $g$, with vertex set $v(g)$ and edge set $e(g)$, are defined as $pi_1(g) = prod_{u in v(g)} {d_u}^2$ and $pi_2(g) = prod_{uv in e(g)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. in this paper we present a simple approach to order these indices for connected graphs on ...

We study graph properties that admit an increasing, or equivalently decreasing, sequence of graphs on the same vertex set such that for any two consecutive graphs in the sequence their difference is a single edge. This is useful for characterizing and computing minimal completions and deletions of arbitrary graphs into having these properties. We prove that threshold graphs and chain graphs adm...

This paper discusses concept chain graphs, a new framework for information retrieval that supports sophisticated contextual queries. Concept chain graphs subsume traditional information retrieval models, but extend them by supporting (i) more sophisticated content representation reflecting information extraction output, and (ii) more sophisticated retrieval algorithms including probabilistic gr...

In this paper, we extend Meek’s conjecture (Meek, 1997) from directed and acyclic graphs to chain graphs, and prove that the extended conjecture is true. Specifically, we prove that if a chain graph H is an independence map of the independence model induced by another chain graph G, then (i) G can be transformed into H by a sequence of directed and undirected edge additions and feasible splits ...

a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.