Related papers: Sparse random graphs with clustering
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…
We propose a model to address the overlooked problem of node clustering in simple hypergraphs. Simple hypergraphs are suitable when a node may not appear multiple times in the same hyperedge, such as in co-authorship datasets. Our model…
We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we…
We present and investigate a general model for inhomogeneous random digraphs with labeled vertices, where the arcs are generated independently, and the probability of inserting an arc depends on the labels of its endpoints and its…
Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this…
We study the evolution of graphs densifying by adding edges: Two vertices are chosen randomly, and an edge is (i) established if each vertex belongs to a tree; (ii) established with probability $p$ if only one vertex belongs to a tree;…
In recent years hypergraphs have emerged as a powerful tool to study systems with multi-body interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the…
Subgraphs such as cliques, loops and stars form crucial connections in the topologies of real-world networks. Random graph models provide estimates for how often certain subgraphs appear, which in turn can be tested against real-world…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
High-dimensional data analysis typically focuses on low-dimensional structure, often to aid interpretation and computational efficiency. Graphical models provide a powerful methodology for learning the conditional independence structure in…
Recent years have witnessed the impressive progress in Neural Dependency Parsing. According to the different factorization approaches to the graph joint probabilities, existing parsers can be roughly divided into autoregressive and…
In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly…
We consider random hyperbolic graphs in hyperbolic spaces of any dimension $d+1\geq 2$. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving…
In this paper we consider the Erd\H{o}s-R\'enyi random graph in the sparse regime in the limit as the number of vertices $n$ tends to infinity. We are interested in what this graph looks like when it contains many triangles, in two…
A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is…
In this paper, we obtain a precise estimate of the probability that the sparse binomial random graph contains a large number of vertices in a triangle. The estimate of log of this probability is correct up to second order, and enables us to…
We consider self-loops and multiple edges in the configuration model as the size of the graph tends to infinity. The interest in these random variables is due to the fact that the configuration model, conditioned on being simple, is a…
We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…