Related papers: Hypothesis Testing for Equality of Latent Position…

In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…

Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph…

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.…

We propose a one-step procedure to estimate the latent positions in random dot product graphs efficiently. Unlike the classical spectral-based methods such as the adjacency and Laplacian spectral embedding, the proposed one-step procedure…

Community detection is a fundamental problem in complex network data analysis. Though many methods have been proposed, most existing methods require the number of communities to be the known parameter, which is not in practice. In this…

We investigate symmetric edge polytopes generated by Erd\H{o}s--R\'enyi random graphs in a high-dimensional regime. These objects provide a natural and largely unexplored model of random lattice polytopes, in which geometric properties are…

We consider a random partition of the vertex set of an arbitrary graph that can be sampled using loop-erased random walks stopped at a random independent exponential time of parameter $q>0$, that we see as a tuning parameter.The related…

Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we…

Many popular dimensionality reduction procedures have out-of-sample extensions, which allow a practitioner to apply a learned embedding to observations not seen in the initial training sample. In this work, we consider the problem of…

Using exact numerical diagonalization, we investigate localization in two classes of random matrices corresponding to random graphs. The first class comprises the adjacency matrices of Erdos-Renyi (ER) random graphs. The second one…

We investigate the problem of detecting correlation between two Erd\H{o}s-R\'enyi graphs $G(n,p)$, formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are independent, while under the alternative…

This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…

We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block…

Statistically equivalent blocks are not frequently considered in the context of nonparametric two-sample hypothesis testing. Despite the limited exposure, this paper shows that a number of classical nonparametric hypothesis tests can be…

We study the stochastic block model with two communities where vertices contain side information in the form of a vertex label. These vertex labels may have arbitrary label distributions, depending on the community memberships. We analyze a…

We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…

The classical setting of community detection consists of networks exhibiting a clustered structure. To more accurately model real systems we consider a class of networks (i) whose edges may carry labels and (ii) which may lack a clustered…

Consider a random graph model with $n$ vertices where each vertex has a vertex-type drawn from some discrete distribution. Suppose that the number of arcs to be placed between each pair of vertex-types is known, and that each arc is placed…

We study the problem of testing for structure in networks using relations between the observed frequencies of small subgraphs. We consider the statistics \begin{align*} T_3 & =(\text{edge frequency})^3 - \text{triangle frequency}\\ T_2 &…

We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when…