English
Related papers

Related papers: Detection and Reconstruction of a Random Hypergrap…

200 papers

The network reconstruction task aims to estimate a complex system's structure from various data sources such as time series, snapshots, or interaction counts. Recent work has examined this problem in networks whose relationships involve…

Social and Information Networks · Computer Science 2023-12-05 Simon Lizotte , Jean-Gabriel Young , Antoine Allard

Random hypergraphs extend the classical notion of random graphs by allowing hyperedges to join more than two vertices, making them well-suited for modeling higher-order interactions in complex systems. Despite their broad applicability,…

Probability · Mathematics 2026-04-08 Yanna J. Kraakman , Clara Stegehuis

The basic inverse problem in spectral graph theory consists in determining the graph given its eigenvalue spectrum. In this paper, we are interested in a network of technological agents whose graph is unknown, communicating by means of a…

Mathematical Physics · Physics 2013-08-20 Enzo Fioriti , Stefano Chiesa , Fabio Fratichini

Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…

Methodology · Statistics 2025-09-16 Yichao Chen , Jingfei Zhang , Ji Zhu

A metric graph is a 1-dimensional stratified metric space consisting of vertices and edges or loops glued together. Metric graphs can be naturally used to represent and model data that take the form of noisy filamentary structures, such as…

Statistics Theory · Mathematics 2014-02-10 Fabrizio Lecci , Alessandro Rinaldo , Larry Wasserman

We consider the problem of inferring a matching hidden in a weighted random $k$-hypergraph. We assume that the hyperedges' weights are random and distributed according to two different densities conditioning on the fact that they belong to…

Disordered Systems and Neural Networks · Physics 2022-11-11 Urte Adomaityte , Anshul Toshniwal , Gabriele Sicuro , Lenka Zdeborová

Graph is an important data representation ubiquitously existing in the real world. However, analyzing the graph data is computationally difficult due to its non-Euclidean nature. Graph embedding is a powerful tool to solve the graph…

Cryptography and Security · Computer Science 2021-10-07 Zhikun Zhang , Min Chen , Michael Backes , Yun Shen , Yang Zhang

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…

Information Theory · Computer Science 2016-11-18 A. G. D'yachkov , I. V. Vorobyev , N. A. Polyanskii , V. Yu. Shchukin

Detecting intrusions in network traffic is a challenging task, particularly under limited supervision and constantly evolving attack patterns. While recent works have leveraged graph neural networks for network intrusion detection, they…

Machine Learning · Computer Science 2025-12-23 Lorenzo Guerra , Thomas Chapuis , Guillaume Duc , Pavlo Mozharovskyi , Van-Tam Nguyen

In the anisotropic random geometric graph model, vertices correspond to points drawn from a high-dimensional Gaussian distribution and two vertices are connected if their distance is smaller than a specified threshold. We study when it is…

Statistics Theory · Mathematics 2022-07-01 Matthew Brennan , Guy Bresler , Brice Huang

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…

Statistical Mechanics · Physics 2010-04-27 Allon G. Percus , Gabriel Istrate , Bruno Goncalves , Robert Z. Sumi , Stefan Boettcher

We study the recently introduced problem of finding dense common subgraphs: Given a sequence of graphs that share the same vertex set, the goal is to find a subset of vertices $S$ that maximizes some aggregate measure of the density of the…

Data Structures and Algorithms · Computer Science 2018-02-20 Moses Charikar , Yonatan Naamad , Jimmy Wu

This paper deals with the problem of graph matching or network alignment for Erd\H{o}s--R\'enyi graphs, which can be viewed as a noisy average-case version of the graph isomorphism problem. Let $G$ and $G'$ be $G(n, p)$ Erd\H{o}s--R\'enyi…

Statistics Theory · Mathematics 2022-07-08 Cheng Mao , Mark Rudelson , Konstantin Tikhomirov

Finding frequently occurring subgraph patterns or network motifs in neural architectures is crucial for optimizing efficiency, accelerating design, and uncovering structural insights. However, as the subgraph size increases,…

Machine Learning · Computer Science 2026-02-04 Yikang Yang , Zhengxin Yang , Minghao Luo , Luzhou Peng , Hongxiao Li , Wanling Gao , Lei Wang , Jianfeng Zhan

This paper studies how close random graphs are typically to their expectations. We interpret this question through the concentration of the adjacency and Laplacian matrices in the spectral norm. We study inhomogeneous Erd\"os-R\'enyi random…

Probability · Mathematics 2016-08-10 Can M. Le , Elizaveta Levina , Roman Vershynin

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…

Data Structures and Algorithms · Computer Science 2021-04-28 Reut Levi , Dana Ron , Ronitt Rubinfeld

In this paper, we consider the graph alignment problem, which is the problem of recovering, given two graphs, a one-to-one mapping between nodes that maximizes edge overlap. This problem can be viewed as a noisy version of the well-known…

Machine Learning · Statistics 2022-01-14 Georgina Hall , Laurent Massoulié

Let $X_1,X_2,...$ be an infinite sequence of i.i.d. random vectors distributed exponentially with parameter $\lam .$ For each $y$ and $n\geq 1,$ form a graph $G_n(y)$ with vertex set $V_n = \{X_1,...,X_n\},$ two vertices are connected if…

Probability · Mathematics 2007-05-23 Bhupendra Gupta

Limiting distributions are derived for the sparse connected components that are present when a random graph on $n$ vertices has approximately $\half n$ edges. In particular, we show that such a graph consists entirely of trees, unicyclic…

Probability · Mathematics 2008-02-03 Svante Janson , Donald E. Knuth , Tomasz Łuczak , Boris Pittel

The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…