Related papers: On directed analogues of expander and hyperfinite …
In causal inference on directed acyclic graphs, the orientation of edges is in general only recovered up to Markov equivalence classes. We study Markov equivalence classes of uniformly random directed acyclic graphs. Using a tower…
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…
The galaxies of nonstandard enlargements of conventionally infinite as well as of transfinite graphs are defined, analyzed, and illustrated by some examples. It is then shown that any such enlargement either has exactly one galaxy, its…
We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…
Jaeger's directed cycle double cover conjecture can be formulated as a problem of existence of special perfect matchings in a class of graphs that we call hexagon graphs. In this work, we explore the structure of hexagon graphs. We show…
We construct a sequence of subset partition graphs satisfying the dimension reduction, adjacency, strong adjacency, and endpoint count properties whose diameter has a superlinear asymptotic lower bound. These abstractions of polytope graphs…
From any given sequence of finite or infinite graphs, a nonstandard graph is constructed. The procedure is similar to an ultrapower construction of an internal set from a sequence of subsets of the real line, but now the individual entities…
We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.
We show that, in almost every $n$-vertex random directed graph process, a copy of every possible $n$-vertex oriented cycle will appear strictly before a directed Hamilton cycle does, except of course for the directed cycle itself.…
We establish an Expander Mixing Lemma for directed graphs in terms of the eigenvalues of an associated asymmetric transition probability matrix, extending the classical spectral inequality to the asymmetric setting. As an application, we…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
Similarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We generalise structural and regular equivalences for undirected…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
We consider infinite connected quasi-transitive locally finite graphs and show that every such graph with more than one end is a tree amalgamation of two other such graphs. This can be seen as a graph-theoretical version of Stallings'…
We introduce the problem of Weak Dominance Drawing for general directed acyclic graphs and we show the connection with the linear extension diameter of a partial order P. We present complexity results and bounds.
We introduce a persistent Hochschild homology framework for directed graphs. Hochschild homology groups of (path algebras of) directed graphs vanish in degree $i\geq 2$. To extend them to higher degrees, we introduce the notion of…
In this survey we aim to give a comprehensive overview of results using sublinear expanders. The term sublinear expanders refers to a variety of definitions of expanders, which typically are defined to be graphs $G$ such that every…
We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random…
In this paper we describe a generic scheme for the parallel exploration of directed acyclic graphs starting from one or more `roots' of the graph. Our scheme is designed for graphs with the following properties, (i) discovering neighbors at…
In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These…