Related papers: Random Geometric Graphs on Euclidean Balls
An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
Given an $n\times n$ symmetric matrix $W\in [0,1]^{[n]\times [n]}$, let $\mathcal{G}(n,W)$ be the random graph obtained by independently including each edge $jk$ with probability $W_{jk}$. Given a degree sequence ${\bf d}=(d_1,\ldots,…
We consider a random geometric graph $G(\chi_n, r_n)$, given by connecting two vertices of a Poisson point process $\chi_n$ of intensity $n$ on the unit torus whenever their distance is smaller than the parameter $r_n$. The model is…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Predicting edges in networks is a key problem in social network analysis and involves reasoning about the relationships between nodes based on the structural properties of a network. In particular, link prediction can be used to analyse how…
A random algebraic graph is defined by a group $G$ with a uniform distribution over it and a connection $\sigma:G\longrightarrow[0,1]$ with expectation $p,$ satisfying $\sigma(g)=\sigma(g^{-1}).$ The random graph…
We investigate random graphs on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point carries an independent random mark and given marks and…
We revisit the classic problem of estimating the degree distribution moments of an undirected graph. Consider an undirected graph $G=(V,E)$ with $n$ vertices, and define (for $s > 0$) $\mu_s = \frac{1}{n}\cdot\sum_{v \in V} d^s_v$. Our aim…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and…
We consider the hypothesis testing problem that two vertices $i$ and $j$ of a generalized random dot product graph have the same latent positions, possibly up to scaling. Special cases of this hypothesis test include testing whether two…
A disordered medium is often constructed by $N$ points independently and identically distributed in a $d$-dimensional hyperspace. Characteristics related to the statistics of this system is known as the random point problem. As $d \to…
The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the…
In this paper, we propose a new method to compute the barycenter of large weighted graphs endowed with probability measures on their nodes. We suppose that the edge weights are distances between the nodes and that the probability measure on…
Let $G$ be a random graph on the vertex set $\{1,2,..., n\}$ such that edges in $G$ are determined by independent random indicator variables, while the probability $p_{ij}$ for $\{i,j\}$ being an edge in $G$ is not assumed to be equal.…
This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge…
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when…
Statistical graph models aim at modeling graphs as random realization among a set of possible graphs. One issue is to evaluate whether or not a graph is likely to have been generated by one particular model. In this paper we introduce the…