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We study the graph matching problem in the presence of vertex feature information using shallow graph neural networks. Specifically, given two graphs that are independent perturbations of a single random geometric graph with sparse binary…

Machine Learning · Computer Science 2025-03-12 Suqi Liu , Morgane Austern

While many multiple graph inference methodologies operate under the implicit assumption that an explicit vertex correspondence is known across the vertex sets of the graphs, in practice these correspondences may only be partially or…

Machine Learning · Statistics 2017-09-29 Vince Lyzinski

We investigate contextual graph matching in the Gaussian setting, where both edge weights and node features are correlated across two networks. We derive precise information-theoretic thresholds for exact recovery, and identify conditions…

Machine Learning · Statistics 2026-03-25 Mohammad Hassan Ahmad Yarandi , Luca Ganassali

Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…

Data Structures and Algorithms · Computer Science 2021-08-10 Cheng Mao , Mark Rudelson , Konstantin Tikhomirov

A variety of information processing tasks in practice involve recovering $n$ objects from single-shot graph-based measurements, particularly those taken over the edges of some measurement graph $\mathcal{G}$. This paper concerns the…

Information Theory · Computer Science 2016-08-04 Yuxin Chen , Andrea J. Goldsmith

This paper studies the problem of matching two complete graphs with edge weights correlated through latent geometries, extending a recent line of research on random graph matching with independent edge weights to geometric models.…

Statistics Theory · Mathematics 2022-02-25 Haoyu Wang , Yihong Wu , Jiaming Xu , Israel Yolou

Motivated by the problem of matching two correlated random geometric graphs, we study the problem of matching two Gaussian geometric models correlated through a latent node permutation. Specifically, given an unknown permutation $\pi^*$ on…

Statistics Theory · Mathematics 2026-04-08 Shuyang Gong , Zhangsong Li

This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the…

Data Structures and Algorithms · Computer Science 2024-04-22 Luca Ganassali

Graph alignment - identifying node correspondences between two graphs - is a fundamental problem with applications in network analysis, biology, and privacy research. While substantial progress has been made in aligning correlated…

Information Theory · Computer Science 2026-03-16 Jakob Maier , Laurent Massoulié

We formulate and analyze a heterogeneous random hypergraph model, and we provide an achieveability result for recovery of hyperedges from the observed projected graph. We observe a projected graph which combines random hyperedges across all…

Data Structures and Algorithms · Computer Science 2026-03-03 Alexander Morgan , Chenghao Guo

The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein…

Computation · Statistics 2017-07-18 Efe Onaran , Soledad Villar

We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…

Information Theory · Computer Science 2023-09-12 Joonhyuk Yang , Hye Won Chung

In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…

Probability · Mathematics 2025-10-30 Laurent Massoulié

The problem of computing the vertex expansion of a graph is an NP-hard problem. The current best worst-case approximation guarantees for computing the vertex expansion of a graph are a $O(\sqrt{\log n})$-approximation algorithm due to…

Data Structures and Algorithms · Computer Science 2018-05-25 Anand Louis , Rakesh Venkat

The correlated Erd\"os-R\'enyi random graph ensemble is a probability law on pairs of graphs with $n$ vertices, parametrized by their average degree $\lambda$ and their correlation coefficient $s$. It can be used as a benchmark for the…

Disordered Systems and Neural Networks · Physics 2024-11-21 Andrea Muratori , Guilhem Semerjian

The network alignment (or graph matching) problem refers to recovering the node-to-node correspondence between two correlated networks. In this paper, we propose a network alignment algorithm which works without using a seed set of…

Data Structures and Algorithms · Computer Science 2020-09-29 Mahdi Bozorg , Saber Salehkaleybar , Matin Hashemi

Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…

Information Theory · Computer Science 2015-03-20 Meng Wang , Weiyu Xu , Enrique Mallada , Ao Tang

In this paper we propose a method of proving impossibility results based on applying strong data-processing inequalities to estimate mutual information between sets of variables forming certain Markov random fields. The end result is that…

Information Theory · Computer Science 2020-05-22 Yury Polyanskiy , Yihong Wu

We study the problem of detecting the edge correlation between two random graphs with $n$ unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated;…

Statistics Theory · Mathematics 2021-02-09 Yihong Wu , Jiaming Xu , Sophie H. Yu

For two independent Erd\H{o}s-R\'enyi graphs $\mathbf G(n,p)$, we study the maximal overlap (i.e., the number of common edges) of these two graphs over all possible vertex correspondence. We present a polynomial-time algorithm which finds a…

Probability · Mathematics 2022-10-17 Jian Ding , Hang Du , Shuyang Gong