Related papers: Statistical Limits for Testing Correlation of Hype…

This paper deals with the problem of detecting non-isotropic high-dimensional geometric structure in random graphs. Namely, we study a model of a random geometric graph in which vertices correspond to points generated randomly and…

For a $d$-uniform random hypergraph on $n$ vertices in which hyperedges are included i.i.d.\ so that the average degree in the hypergraph is $n^{\delta+o(1)}$, the projection of such a hypergraph is a graph on the same $n$ vertices where an…

A property of finite graphs is called nondeterministically testable if it has a "certificate" such that once the certificate is specified, its correctness can be verified by random local testing. In this paper we study certificates that…

The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. We give a new characterization of…

In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…

Let $G_1,\dots, G_m$ be independent identically distributed random subgraphs of the complete graph ${\cal K}_n$. We analyse the threshold behaviour of the strength of connectedness of the union $\cup_{i=1}^mG_i$ defined on the vertex set of…

In this paper, we consider the problem of testing the equality of two multivariate distributions based on geometric graphs constructed using the interpoint distances between the observations. These include the tests based on the minimum…

Minimum Label Cut (or Hedge Connectivity) problem is defined as follows: given an undirected graph $G=(V, E)$ with $n$ vertices and $m$ edges, in which, each edge is labeled (with one or multiple labels) from a label set $L=\{\ell_1,\ell_2,…

Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is…

We establish thresholds for the feasibility of random multi-graph alignment in two models. In the Gaussian model, we demonstrate an "all-or-nothing" phenomenon: above a critical threshold, exact alignment is achievable with high…

We introduce two novel non-parametric statistical hypothesis tests. The first test, called the relative test of dependency, enables us to determine whether one source variable is significantly more dependent on a first target variable or a…

This paper studies the propagation connectivity of a random hypergraph $\mathbb{G}$ containing both 2-edges and 3-hyperedges. We find an exact threshold of the propagation connectivity of $\mathbb{G}$: If $I_{\epsilon,r}<-1$, then…

Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…

We derive an asymptotic formula for the number of strongly connected digraphs with $n$ vertices and $m$ arcs (directed edges), valid for $m-n\to\infty$ as $n\to \infty$ provided $m=O(n\log n)$. This fills the gap between Wright's results…

The hypergraph unreliability problem asks for the probability that a hypergraph gets disconnected when every hyperedge fails independently with a given probability. For graphs, the unreliability problem has been studied over many decades,…

We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.

Consider a pair of correlated Erd\H{o}s-R\'enyi graphs $\mathcal G(n,\tfrac{\lambda}{n};s)$ that are subsampled from a common parent Erd\H{o}s-R\'enyi graph with average degree $\lambda$ and subsampling probability $s$. We establish a sharp…

The independence density of a finite hypergraph is the probability that a subset of vertices, chosen uniformly at random contains no hyperedges. Independence densities can be generalized to countable hypergraphs using limits. We show that,…

We obtain new lower bounds for the independence number of $K_r$-free graphs and linear $k$-uniform hypergraphs in terms of the degree sequence. This answers some old questions raised by Caro and Tuza \cite{CT91}. Our proof technique is an…

We study thresholds for the appearance of a 2-core in random hypergraphs that are a mixture of a constant number of random uniform hypergraphs each with a linear number of edges but with different edge sizes. For the case of two overlapping…