Matching Correlated Inhomogeneous Random Graphs using the $k$-core Estimator

• URL: http://arxiv.org/abs/2302.05407v1
• Date: Fri, 10 Feb 2023 18:21:35 GMT
• Title: Matching Correlated Inhomogeneous Random Graphs using the $k$-core Estimator
• Authors: Mikl\'os Z. R\'acz and Anirudh Sridhar
• Abstract summary: We study the so-called emph$k$-core estimator, which outputs a correspondence that induces a large, common subgraph of both graphs. We specialize our general framework to derive new results on exact and partial recovery in correlated block models, correlated Chung-Lu geometric graphs, and correlated random graphs.
• Score: 5.685589351789462
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the task of estimating the latent vertex correspondence between two edge-correlated random graphs with generic, inhomogeneous structure. We study the so-called \emph{$k$-core estimator}, which outputs a vertex correspondence that induces a large, common subgraph of both graphs which has minimum degree at least $k$. We derive sufficient conditions under which the $k$-core estimator exactly or partially recovers the latent vertex correspondence. Finally, we specialize our general framework to derive new results on exact and partial recovery in correlated stochastic block models, correlated Chung-Lu graphs, and correlated random geometric graphs.

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