Related papers: Algorithms for realizing degree sequences of direc…
We consider the following fundamental realization problem of directed graphs. Given a sequence $S:={a_1 \choose b_1},\dots,{a_n \choose b_n}$ with $a_i,b_i\in \mathbb{Z}_0^+.$ Does there exist a digraph (no loops and no parallel arcs are…
In 2006 Qian [J. Qian, Degree complete graphs; Discrete Mathematics 306 (2006), 533--537] introduced the concept of degree complete graphs for labeled graphs. He also gave a characterization of these graphs in terms of two forbidden…
Given the degree sequence $d$ of a graph, the realization graph of $d$ is the graph having as its vertices the labeled realizations of $d$, with two vertices adjacent if one realization may be obtained from the other via an edge-switching…
We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random…
For many types of graphs, criteria have been discovered that give necessary and sufficient conditions for an integer sequence to be the degree sequence of such a graph. These criteria tend to take the form of a set of inequalities, and in…
Clustering is an important topic in algorithms, and has a number of applications in machine learning, computer vision, statistics, and several other research disciplines. Traditional objectives of graph clustering are to find clusters with…
We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify…
Evaluating graphs learned by causal discovery algorithms is difficult: The number of edges that differ between two graphs does not reflect how the graphs differ with respect to the identifying formulas they suggest for causal effects. We…
We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices. Each finite directed acyclic graph admits countably many structures of a generalized…
Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that…
Understanding how the cycles of a graph or digraph behave in general has always been an important point of graph theory. In this paper, we study the question of finding a set of $k$ vertex-disjoint cycles (resp. directed cycles) of distinct…
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…
A new efficient algorithm is presented for finding all simple cycles that satisfy a length constraint in a directed graph. When the number of vertices is non-trivial, most cycle-finding problems are of practical interest for sparse graphs…
We introduce a new class of auto-encoders for directed graphs, motivated by a direct extension of the Weisfeiler-Leman algorithm to pairs of node labels. The proposed model learns pairs of interpretable latent representations for the nodes…
For a degree sequence, we define the set of edges that appear in every labeled realization of that sequence as forced, while the edges that appear in none as forbidden. We examine structure of graphs whose degree sequences contain either…
The question whether there exists a hypergraph whose degrees are equal to a given sequence of integers is a well-known reconstruction problem in graph theory, which is motivated by discrete tomography. In this paper we approach the problem…
A finite non-increasing sequence of positive integers $d = (d_1\geq \cdots\geq d_n)$ is called a degree sequence if there is a graph $G = (V,E)$ with $V = \{v_1,\ldots,v_n\}$ and $deg(v_i)=d_i$ for $i=1,\ldots,n$. In that case we say that…
We give characterizations of the structure and degree sequences of hereditary unigraphs, those graphs for which every induced subgraph is the unique realization of its degree sequence. The class of hereditary unigraphs properly contains the…
We report on recent advances in rule-based graph programming, which allow us to match the time complexity of some fundamental imperative graph algorithms. In general, achieving the time complexity of graph algorithms implemented in…
There are typically several nonisomorphic graphs having a given degree sequence, and for any two degree sequence terms it is often possible to find a realization in which the corresponding vertices are adjacent and one in which they are…