Related papers: The Phantom Alignment Strength Conjecture: Practic…
When two graphs have a correlated Bernoulli distribution, we prove that the alignment strength of their natural bijection strongly converges to a novel measure of graph correlation $\rho_T$ that neatly combines intergraph with intragraph…
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…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
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…
Graph matching is the process of computing the similarity between two graphs. Depending on the requirement, it can be exact or inexact. Exact graph matching requires a strict correspondence between nodes of two graphs, whereas inexact…
In a 1977 paper, Steffens identified an elegant criterion for determining when a countable graph has a perfect matching. In this paper, we will investigate the proof-theoretic strength of this result and related theorems. We show that a…
Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this…
Classical graph matching aims to find a node correspondence between two unlabeled graphs of known topologies. This problem has a wide range of applications, from matching identities in social networks to identifying similar biological…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to…
Graph pattern mining methods can extract informative and useful patterns from large-scale graphs and capture underlying principles through the overwhelmed information. Contrast analysis serves as a keystone in various fields and has…
Graph-level contrastive learning, aiming to learn the representations for each graph by contrasting two augmented graphs, has attracted considerable attention. Previous studies usually simply assume that a graph and its augmented graph as a…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
Network alignment is a problem of finding the node mapping between similar networks. It links the data from separate sources and is widely studied in bioinformation and social network fields. The critical difference between network…
Regression on observational data can fail to capture a causal relationship in the presence of unobserved confounding. Confounding strength measures this mismatch, but estimating it requires itself additional assumptions. A common assumption…
Database alignment is a variant of the graph alignment problem: Given a pair of anonymized databases containing separate yet correlated features for a set of users, the problem is to identify the correspondence between the features and…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
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…
Motivated by alignment of correlated sparse random graphs, we introduce a hypothesis testing problem of deciding whether or not two random trees are correlated. We obtain sufficient conditions under which this testing is impossible or…