Related papers: A structural Markov property for decomposable grap…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of…
We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…
The family of $\mathfrak{I}$-contractible graphs and contractible transformations was defined by A. Ivashchenko in the mid-90's. In this paper we study the collapsibility and homological properties of the clique complex associated to…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
Probabilistic circuits (PCs) represent a probability distribution as a computational graph. Enforcing structural properties on these graphs guarantees that several inference scenarios become tractable. Among these properties, structured…
A clique coloring of a graph is an assignment of colors to its vertices such that no maximal clique is monochromatic. We initiate the study of structural parameterizations of the Clique Coloring problem which asks whether a given graph has…
Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology…
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of…
In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may…
We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…
We describe structural properties of strongly connected finite directed graphs, that are invariants of the topological conjugacy of their Markov-Dyck shifts. For strongly connected finite directed graphs with these properties topological…
A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures…
We introduce a new definition of exponential family of Markov chains, and show that many characteristic properties of the usual exponential family of probability distributions are properly extended to Markov chains. The method of…
The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…
A bipartite graph $H$ is said to have Sidorenko's property if the probability that the uniform random mapping from $V(H)$ to the vertex set of any graph $G$ is a homomorphism is at least the product over all edges in $H$ of the probability…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
We propose the n-clique network as a powerful tool for understanding global structures of combined highly-interconnected subgraphs, and provide theoretical predictions for statistical properties of the n-clique networks embedded in a…
Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and…