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In this paper, we study the problem of recovering the latent vertex correspondence between two correlated random graphs with vastly inhomogeneous and unknown edge probabilities between different pairs of vertices. Inspired by and extending…

Data Structures and Algorithms · Computer Science 2025-08-19 Jian Ding , Yumou Fei , Yuanzheng Wang

The detection of anomalous activity in graphs is a statistical problem that arises in many applications, such as network surveillance, disease outbreak detection, and activity monitoring in social networks. Beyond its wide applicability,…

Machine Learning · Statistics 2013-12-12 James Sharpnack , Akshay Krishnamurthy , Aarti Singh

There are many methods to estimate the quasi-stationary infected fraction of the SIS process on (random) graphs. A challenge is to adequately incorporate correlations, which is especially important in sparse graphs. Methods typically are…

Statistical Mechanics · Physics 2024-11-18 O. S. Awolude , H. Don , E. Cator

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…

Physics and Society · Physics 2010-04-14 Charo I. Del Genio , Hyunju Kim , Zoltan Toroczkai , Kevin E. Bassler

We consider the problem of estimating a vector of discrete variables $(\theta_1,\cdots,\theta_n)$, based on noisy observations $Y_{uv}$ of the pairs $(\theta_u,\theta_v)$ on the edges of a graph $G=([n],E)$. This setting comprises a broad…

Probability · Mathematics 2019-09-24 Ahmed El Alaoui , Andrea Montanari

We formalize the problem of detecting the presence of a botnet in a network as an hypothesis testing problem where we observe a single instance of a graph. The null hypothesis, corresponding to the absence of a botnet, is modeled as a…

Statistics Theory · Mathematics 2021-04-16 Gianmarco Bet , Kay Bogerd , Rui M. Castro , Remco van der Hofstad

This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of…

Probability · Mathematics 2021-03-08 James MacLaurin

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

A significant problem in analysis of complex network is to reveal community structure, in which network nodes are tightly connected in the same communities, between which there are sparse connections. Previous algorithms for community…

Physics and Society · Physics 2018-04-25 Jingming Zhang , Jianjun Cheng , Xing Su , Xinhong Yin , Shiyan Zhao , Xiaoyun Chen

The independence gap of a graph was introduced by Ekim et al. (2018) as a measure of how far a graph is from being well-covered. It is defined as the difference between the maximum and minimum size of a maximal independent set. We…

Combinatorics · Mathematics 2018-12-14 Tınaz Ekim , Didem Gözüpek , Ademir Hujdurović , Martin Milanič

We introduce a new conjecture on the computational hardness of detecting random lifts of graphs: we claim that there is no polynomial-time algorithm that can distinguish between a large random $d$-regular graph and a large random lift of a…

Computational Complexity · Computer Science 2024-04-29 Dmitriy Kunisky , Xifan Yu

To understand how hidden information can be extracted from statistical networks, planted models in random graphs have been the focus of intensive study in recent years. In this work, we consider the detection of a planted matching, i.e., an…

Statistics Theory · Mathematics 2025-12-17 Timothy L. H. Wee , Cheng Mao

Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For $n$-vertex and $m$-edge graphs, the best known algorithms run in…

Data Structures and Algorithms · Computer Science 2021-05-10 Tomohiro Koana , Viatcheslav Korenwein , André Nichterlein , Rolf Niedermeier , Philipp Zschoche

Two-sample hypothesis testing for large graphs is popular in cognitive science, probabilistic machine learning and artificial intelligence. While numerous methods have been proposed in the literature to address this problem, less attention…

Methodology · Statistics 2024-02-20 Xin Jin , Kit Chan , Ian Barnett , Riddhi Pratim Ghosh

Random graphs are statistical models that have many applications, ranging from neuroscience to social network analysis. Of particular interest in some applications is the problem of testing two random graphs for equality of generating…

Methodology · Statistics 2024-01-08 Anton A. Alyakin , Joshua Agterberg , Hayden S. Helm , Carey E. Priebe

Graph matching is an important problem in machine learning and pattern recognition. Herein, we present theoretical and practical results on the consistency of graph matching for estimating a latent alignment function between the vertex sets…

Optimization and Control · Mathematics 2014-08-04 Vince Lyzinski , Donniell E. Fishkind , Carey E. Priebe

Graphs are powerful abstractions for capturing complex relationships in diverse application settings. An active area of research focuses on theoretical models that define the generative mechanism of a graph. Yet given the complexity and…

Social and Information Networks · Computer Science 2016-09-19 Rajmonda S. Caceres , Leah Weiner , Matthew C. Schmidt , Benjamin A. Miller , William M. Campbell

We study the problem of learning the causal relationships between a set of observed variables in the presence of latents, while minimizing the cost of interventions on the observed variables. We assume access to an undirected graph $G$ on…

Data Structures and Algorithms · Computer Science 2020-12-29 Raghavendra Addanki , Andrew McGregor , Cameron Musco

Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…

Discrete Mathematics · Computer Science 2022-07-04 Timo Gervens , Martin Grohe

We study information-theoretic phase transitions for the detectability of latent geometry in bipartite random geometric graphs RGGs with Gaussian d-dimensional latent vectors while only a subset of edges carries latent information…

Probability · Mathematics 2026-04-13 Andreas Göbel , Marcus Pappik , Leon Schiller