Related papers: Exact alignment recovery for correlated Erd\H{o}s-…
We consider the problem of perfectly recovering the vertex correspondence between two correlated Erd\H{o}s-R\'enyi (ER) graphs. For a pair of correlated graphs on the same vertex set, the correspondence between the vertices can be obscured…
This paper studies the problem of recovering the hidden vertex correspondence between two correlated random graphs. We propose the partially correlated Erd\H{o}s-R\'enyi graphs model, wherein a pair of induced subgraphs with a certain…
For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}.…
This paper studies the problem of recovering the hidden vertex correspondence between two edge-correlated random graphs. We focus on the Gaussian model where the two graphs are complete graphs with correlated Gaussian weights and the…
We determine information theoretic conditions under which it is possible to partially recover the alignment used to generate a pair of sparse, correlated Erd\H{o}s-R\'enyi graphs. To prove our achievability result, we introduce the $k$-core…
Random graph alignment refers to recovering the underlying vertex correspondence between two random graphs with correlated edges. This can be viewed as an average-case and noisy version of the well-known graph isomorphism problem. For the…
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…
Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs of $n$ vertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erd\H{o}s-R\'enyi…
This work studies fundamental limits for recovering the underlying correspondence among multiple correlated graphs. In the setting of inhomogeneous random graphs, we present and analyze a matching algorithm: first partially match the graphs…
Graph matching problem aims to identify node correspondence between two or more correlated graphs. Previous studies have primarily focused on models where only edge information is provided. However, in many social networks, not only the…
We study graph matching between two correlated networks in the almost fully seeded regime, where all but a vanishing fraction of vertex correspondences are revealed. Concretely, we consider the correlated stochastic block model and assume…
For two unlabeled graphs $G_1,G_2$ independently sub-sampled from an Erd\H{o}s-R\'enyi graph $\mathbf G(n,p)$ by keeping each edge with probability $s$, we aim to recover \emph{as many as possible} of the corresponding vertex pairs. We…
In this paper, we propose a family of label recovery problems on weighted Euclidean random graphs. The vertices of a graph are embedded in $\mathbb{R}^d$ according to a Poisson point process, and are assigned to a discrete community label.…
The graph alignment problem aims to identify the vertex correspondence between two correlated graphs. Most existing studies focus on the scenario in which the two graphs share the same vertex set. However, in many real-world applications,…
We consider the task of learning latent community structure from multiple correlated networks. First, we study the problem of learning the latent vertex correspondence between two edge-correlated stochastic block models, focusing on the…
The problem of detecting edge correlation between two Erd\H{o}s-R\'enyi random graphs on $n$ unlabeled nodes can be formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are sampled independently; under the…
Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in…
We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. Extending the exact recovery…
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…
Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…