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.

翻译：我们考虑估计两个具有一般非齐次结构的边相关随机图中潜在顶点对应关系的任务。我们研究所谓的\emph{$k$-核估计量}，该估计量输出一个顶点对应关系，使得两个图产生一个最小度至少为$k$的大型公共子图。我们推导了$k$-核估计量精确或部分恢复潜在顶点对应关系的充分条件。最后，我们将一般框架具体化，推导出相关随机块模型、相关Chung-Lu图和相关随机几何图中精确恢复与部分恢复的新结果。