相关论文: The GHS and other correlation inequalities for the…
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…
In this paper, we explore the two-star Exponential Random Graph Model, which is a two parameter exponential family on the space of simple labeled graphs. We introduce auxiliary variables to express the two-star model as a mixture of the…
Edge expansion is a parameter indicating how well-connected a graph is. It is useful for designing robust networks, analysing random walks or information flow through a network and is an important notion in theoretical computer science.…
We introduce a new model of correlated randomly growing graphs and study the fundamental questions of detecting correlation and estimating aspects of the correlated structure. The model is simple and starts with any model of randomly…
The edge-degeneracy model is an exponential random graph model that uses the graph degeneracy, a measure of the graph's connection density, and number of edges in a graph as its sufficient statistics. We show this model is relatively…
The inducibility of a graph $H$ measures the maximum number of induced copies of $H$ a large graph $G$ can have. Generalizing this notion, we study how many induced subgraphs of fixed order $k$ and size $\ell$ a large graph $G$ on $n$…
The classical random graph model $G(n,\lambda/n)$ satisfies a `duality principle', in that removing the giant component from a supercritical instance of the model leaves (essentially) a subcritical instance. Such principles have been proved…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
We consider the following question. We have a dense regular graph $G$ with degree $\alpha n$, where $\alpha>0$ is a constant. We add $m=o(n^2)$ random edges. The edges of the augmented graph $G(m)$ are given independent edge weights $X(e)$,…
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…
Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average correlation between the…
Exponential random graph models (ERGMs) are flexible probability models allowing edge dependency. However, it is known that, to a first-order approximation, many ERGMs behave like Erd\"os-R\'enyi random graphs, where edges are independent.…
We study the asymptotics of large simple graphs constrained by the limiting density of edges and the limiting subgraph density of an arbitrary fixed graph $H$. We prove that, for all but finitely many values of the edge density, if the…
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…
The symmetric difference of two graphs $G_1,G_2$ on the same set of vertices $[n]=\{1,2, \ldots ,n\}$ is the graph on $[n]$ whose set of edges are all edges that belong to exactly one of the two graphs $G_1,G_2$. Let $H$ be a fixed graph…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
We show that for an infinitely many natural numbers $k$ there are $k$-uniform hypergraphs which admit a `rescaling phenomenon' as described in [9]. More precisely, let $\mathcal{A}(k,I, n)$ denote the class of $k$-graphs on $n$ vertices in…
We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the limiting probability distribution and the…
Consider a discrete locally finite subset $\Gamma$ of $R^d$ and the complete graph $(\Gamma,E)$, with vertices $\Gamma$ and edges $E$. We consider Gibbs measures on the set of sub-graphs with vertices $\Gamma$ and edges $E'\subset E$. The…
The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of…