Related papers: Markov properties for mixed graphs

In his survey "Beyond graph energy: Norms of graphs and matrices" (2016), Nikiforov proposed two problems concerning characterizing the graphs that attain equality in a lower bound and in a upper bound for the energy of a graph,…

Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…

We present the main concepts and results for Graph Directed Markov Systems that have a finitely irreducible incidence matrix. We then see how these results change when the incidence matrix is not assumed to be finitely irreducible.

The imsets of Studen\'y (2005) are an algebraic method for representing conditional independence models. They have many attractive properties when applied to such models, and they are particularly nice for working with directed acyclic…

A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide, to the best of our knowledge, the first characterization of…

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series…

Independence complexes of circle graphs are purely combinatorial objects. However, when constructed from some diagram of a link $L$, they reveal topological properties of $L$, more specifically, of its Khovanov homology. We analyze the…

Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and…

We extend the notion of a tree graph to sequences of prime graphs which are cycles and edges and name these non-chordal graphs hollow trees. These structures are especially attractive for palindromic Ising models, which mimic a symmetry of…

We characterise the structure of those graphs of a given order which maximise the number of connected induced subgraphs for seven different graph classes, each with other prescribed parameters like minimum degree, independence number,…

The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without…

We construct a family of maximal linklessly embeddable graphs on $n$ vertices and $3n-5$ edges for all $n\ge 10$, and another family on $n$ vertices and $m< \frac{25n}{12}-\frac{1}{4}$ edges for all $n\ge 13$. The latter significantly…

We consider topological Markov chains (also called Markov shifts) on countable graphs. We show that a transient graph can be extended to a recurrent graph of equal entropy which is either positive recurrent of null recurrent, and we give an…

Consider a graph on the non-singular matrices over a finite field, in which two distinct non-singular matrices are joined by an edge whenever their sum is singular. We prove an upper bound for the independence number of this graph. As a…

A maximal independent set in a graph $G$ is an independent set that cannot be extended to a larger independent set by adding any vertex from $G$. This paper investigates the problem of determining the maximum number of maximal independent…

Random walks on graphs are a fundamental concept in graph theory and play a crucial role in solving a wide range of theoretical and applied problems in discrete math, probability, theoretical computer science, network science, and machine…

We have generalised the concept of graph states to what we have called mixed graph states, which we define in terms of mixed graphs, that is graphs with both directed and undirected edges, as the density matrix stabilized by the associated…

We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully…

This work addresses the following question: Under what assumptions on the data generating process can one infer the causal graph from the joint distribution? The approach taken by conditional independence-based causal discovery methods is…

Markoff mod-$p$ graphs are conjectured to be connected for all primes $p$. In this paper, we use results of Chen and Bourgain, Gamburd, and Sarnak to confirm the conjecture for all $p > 3.448\cdot10^{392}$. We also provide a method that…