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We consider the ensemble of adjacency matrices of Erd{\H o}s-R\'enyi random graphs, i.e.\ graphs on $N$ vertices where every edge is chosen independently and with probability $p \equiv p(N)$. We rescale the matrix so that its bulk…
We study the intersection of a random geometric graph with an Erd\H{o}s-R\'enyi graph. Specifically, we generate the random geometric graph $G(n, r)$ by choosing $n$ points uniformly at random from $D=[0, 1]^2$ and joining any two points…
In this paper, we propose second-order graph-based neural dependency parsing using message passing and end-to-end neural networks. We empirically show that our approaches match the accuracy of very recent state-of-the-art second-order…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
Exponential-family random graph models (ERGMs) are a family of network models originating in social network analysis, which have also been applied to biological networks. Advances in estimation algorithms have increased the practical scope…
In dense Erd\H{o}s-R\'enyi random graphs, we are interested in the events where large numbers of a given subgraph occur. The mean behavior of subgraph counts is known, and only recently were the related large deviations results discovered.…
We consider eigenvectors of adjacency matrices of Erd\H{o}s-R\'{e}nyi graphs and study the variation of their directions by resampling the entries randomly. Let $\mathbf{v}$ be the eigenvector associated with the second-largest eigenvalue…
The problem of detecting edge correlation between two Erd\H{o}s-R\'enyi random graphs on $n$ unlabeled nodes can be formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are sampled independently; under the…
The unconstrained exponential family of random graphs assumes no prior knowledge of the graph before sampling, but it is natural to consider situations where partial information about the graph is known, for example the total number of…
In this article we find exponential good approximation of the empirical neigbourhood distribution of symbolled random graphs conditioned to a given empirical symbol distribution and empirical pair distribution. Using this approximation we…
In this paper we consider a dynamic Erd\H{o}s-R\'enyi graph in which edges, according to an alternating renewal process, change from present to absent and vice versa. The objective is to estimate the on- and off-time distributions while…
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…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
Exponential Random Graph Models (ERGMs) have gained increasing popularity over the years. Rooted into statistical physics, the ERGMs framework has been successfully employed for reconstructing networks, detecting statistically significant…
We consider the random geometric graph on $n$ vertices drawn uniformly from a $d$--dimensional sphere. We focus on the sparse regime, when the expected degree is constant independent of $d$ and $n$. We show that, when $d$ is larger than $n$…
We use the exponential random graph models to understand the network structure and its generative process for the Japanese bipartite network of banks and firms. One of the well known and simple model of exponential random graph is the…
Networks are ubiquitous in economic research on organizations, trade, and many other areas. However, while economic theory extensively considers networks, no general framework for their empirical modeling has yet emerged. We thus introduce…
Exponential-family random graph models (ERGMs) are probabilistic network models that are parametrized by sufficient statistics based on structural (i.e., graph-theoretic) properties. The ergm package for the R statistical computing system…
We study the efficient generation of random graphs with a prescribed expected degree sequence, focusing on rank-1 inhomogeneous models in which vertices are assigned weights and edges are drawn independently with probabilities proportional…