Related papers: Random Recursive Hypergraphs
We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…
In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…
The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and…
We study a one parameter family of random graph models that spans a continuum between traditional random graphs of the Erd\H{o}s-R\'enyi type, where there is no underlying structure, and percolation models, where the possible edges are…
For the simple Bratteli diagrams B where there is a single edge connecting any two vertices in consecutive levels, we show that a random order has uncountably many infinite paths if and only if the growth rate of the level-n vertex sets is…
In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they…
A rainbow subgraph of an edge-coloured graph has all edges of distinct colours. A random d-regular graph with d even, and having edges coloured randomly with d/2 of each of n colours, has a rainbow Hamilton cycle with probability tending to…
We present a method for generating random hypergraphs in context-free hypergraph languages. It is obtained by adapting Mairson's generation algorithm for context-free string grammars to the setting of hyperedge replacement grammars. Our…
We comment on old and new results related to the destruction of a random recursive tree (RRT), in which its edges are cut one after the other in a uniform random order. In particular, we study the number of steps needed to isolate or…
Networks are a powerful abstraction with applicability to a variety of scientific fields. Models explaining their morphology and growth processes permit a wide range of phenomena to be more systematically analysed and understood. At the…
We give several results showing that different discrete structures typically gain certain spanning substructures (in particular, Hamilton cycles) after a modest random perturbation. First, we prove that adding linearly many random edges to…
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…
Let a random geometric graph be defined in the supercritical regime for the existence of a unique infinite connected component in Euclidean space. Consider the first-passage percolation model with independent and identically distributed…
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…
The theme of this paper is the derivation of analytic formulae for certain large combinatorial structures. The formulae are obtained via fluid limits of pure jump type Markov processes, established under simple conditions on the Laplace…
The jump graph $J(G)$ of a simple graph $G$ has vertices which represent edges in $G$ where two vertices in $J(G)$ are adjacent if and only if the corresponding edges in $G$ do not share an endpoint. In this paper, we examine sequences of…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
This paper proposes an autoregressive (AR) model for sequences of graphs, which generalises traditional AR models. A first novelty consists in formalising the AR model for a very general family of graphs, characterised by a variable…
The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…
Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial,…