Related papers: Projective limits of probabilistic symmetries and …
We study the joint degree counts in proportional attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p…
In recent years, a growing number of method and application works have adapted and applied the causal-graphical-model framework to time series data. Many of these works employ time-resolved causal graphs that extend infinitely into the past…
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay…
Our goal is to develop a limit approach for a class of problems in additive combinatorics that is analogous to the limit theory of dense graph sequences. We introduce metric, convergence and limit objects for functions on groups and for…
We introduce and study analogues of expander and hyperfinite graph sequences in the context of directed acyclic graphs, which we call "extender" and "hypershallow" graph sequences, respectively. Our main result is a probabilistic…
Given a group $G$, the model $\mathcal{G}(G,p)$ denotes the probability space of all Cayley graphs of $G$ where each element of $G$ is included in the generating set independently at random with probability $p$. In this article, we…
Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…
In this paper, we study convergence of coupled dynamical systems on convergent sequences of graphs to a continuum limit. We show that the solutions of the initial value problem for the dynamical system on a convergent graph sequence tend to…
We study topological and geometric functionals of $l_\infty$-random geometric graphs on the high-dimensional torus in a sparse regime, where the expected number of neighbors decays exponentially in the dimension. More precisely, we…
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…
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted…
Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles under the constraints that the expected values of a set of graph observables are equal to given…
Given a dense countable set in a metric space, the infinite random geometric graph is the random graph with the given vertex set and where any two points at distance less than 1 are connected, independently, with some fixed probability. It…
Let $G = (V,E)$ be a connected directed graph on $n$ vertices. Assign values from the set $\{1,2,\dots,n\}$ to the vertices of $G$ and update the values according to the following rule: uniformly at random choose a vertex and update its…
The goal of the paper is to lay the foundation for the qualitative analogue of the classical, quantitative sparse graph limit theory. In the first part of the paper we introduce the qualitative analogues of the Benjamini-Schramm and…
We consider limit probabilities of first order properties in random graphs with a given degree sequence. Under mild conditions on the degree sequence, we show that the closure set of limit probabilities is a finite union of closed…
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…
We explore graph theoretical properties of minimal prime graphs of finite solvable groups. In finite group theory studying the prime graph of a group has been an important topic for the past almost half century. Recently prime graphs of…
A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…
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…