Related papers: Detection of local geometry in random graphs: info…
We pursue the study of edge-irregulators of graphs, which were recently introduced in [Fioravantes et al. Parametrised Distance to Local Irregularity. IPEC, 2024]. That is, we are interested in the parameter Ie(G), which, for a given graph…
We study a generalization of the classical hidden clique problem to graphs with real-valued edge weights. Formally, we define a hypothesis testing problem. Under the null hypothesis, edges of a complete graph on $n$ vertices are associated…
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…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…
This paper presents an edge detection method based on global and local parameters of the image, which produces satisfactory results on the edge detection of complex images and has a simple structure for execution. The local and global…
In this paper, we prove a local limit theorem for the distribution of the number of triangles in the Erdos-Renyi random graph $G(n,p)$, where $p \in (0,1)$ is a fixed constant. Our proof is based on bounding the characteristic function…
A random geometric digraph $G_n$ is constructed by taking $\{X_1,X_2,... X_n\}$ in $\mathbb{R}^2$ independently at random with a common bounded density function. Each vertex $X_i$ is assigned at random a sector $S_i$ of central angle…
In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…
k-connectivity of random graphs is a fundamental property indicating reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of sensor nodes with limited power resources are modeled by random graphs with unreliable nodes,…
Given two graphs $G$ and $H$, we investigate for which functions $p=p(n)$ the random graph $G_{n,p}$ (the binomial random graph on $n$ vertices with edge probability $p$) satisfies with probability $1-o(1)$ that every red-blue-coloring of…
We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a…
In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…
One-dimensional geometric random graphs are constructed by distributing $n$ nodes uniformly and independently on a unit interval and then assigning an undirected edge between any two nodes that have a distance at most $r_n$. These graphs…
Random graphs are mathematical models that have applications in a wide range of domains. We study the following model where one adds Erd\H{o}s--R\'enyi (ER) type perturbation to a random geometric graph. More precisely, assume…
Several probabilistic models from high-dimensional statistics and machine learning reveal an intriguing --and yet poorly understood-- dichotomy. Either simple local algorithms succeed in estimating the object of interest, or even…
We study the problem of community detection (CD) on Euclidean random geometric graphs where each vertex has two latent variables: a binary community label and a $\mathbb{R}^d$ valued location label which forms the support of a Poisson point…
Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph $H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we focus our attention…
In the distributed triangle detection problem, we have an $n$-vertex network $G=(V,E)$ with one player for each vertex of the graph who sees the edges incident on the vertex. The players communicate in synchronous rounds using the edges of…
Recently, variants of many classical extremal theorems have been proved in the random environment. We, complementing existing results, extend the Erd\H{o}s-Gallai Theorem in random graphs. In particular, we determine, up to a constant…
We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…