Related papers: Scaling limits of random graphs

This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…

In this paper we explore maximal deviations of large random structures from their typical behavior. We introduce a model for a high-dimensional random graph process and ask analogous questions to those of Vapnik and Chervonenkis for…

We analyse the scaling limit of the sizes of the largest components of the Random Intersection Graph $G(n,m,p)$ close to the critical point $p=\frac{1}{\sqrt{nm}}$, when the numbers $n$ of individuals and $m$ of communities have different…

We present a new technique for proving logarithmic upper bounds for diameters of evolving random graph models, which is based on defining a coupling between random graphs and variants of random recursive trees. The advantage of the…

The problem of defining a statistical ensemble of random graphs with an arbitrary connectivity distribution is discussed. Introducing such an ensemble is a step towards uderstanding the geometry of wide classes of graphs independently of…

We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…

We study random $k$-connected chordal graphs with bounded tree-width. Our main results are scaling limits and quenched local limits.

Local convergence of bounded degree graphs was introduced by Benjamini and Schramm. This result was extended further by Lyons to bounded average degree graphs. In this paper we study the convergence of random tree sequences with given…

In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent…

We consider events over the probability space generated by the degree sequences of multiple independent Erd\H{o}s-R\'enyi random graphs, and consider an approximation probability space where such degree sequences are deemed to be sequences…

We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We…

The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.

We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…

We examine maximum vertex coloring of random geometric graphs, in an arbitrary but fixed dimension, with a constant number of colors. Since this problem is neither scale-invariant nor smooth, the usual methodology to obtain limit laws…

The bloom of complex network study, in particular, with respect to scale-free ones, is considerably triggering the research of scale-free graph itself. Therefore, a great number of interesting results have been reported in the past,…

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…

We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding…

We study a model of random $\mathcal{R}$-enriched trees that is based on weights on the $\mathcal{R}$-structures and allows for a unified treatment of a large family of random discrete structures. We establish distributional limits…

We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…

The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in…