标题： 具有节点属性的相关网络中的精确匹配以改进社区恢复 显示英文标题

标题： Exact Matching in Correlated Networks with Node Attributes for Improved Community Recovery

摘要： 我们研究了节点和边联合相关的多重网络中的社区检测问题。 这种设定自然出现在诸如社交平台的应用中，其中共享的一组用户可能在不同平台上表现出既相关又具有关联特性的友谊模式。 通过扩展经典的随机块模型（SBM）及其上下文版本（CSBM），我们引入了相关联的CSBM，该模型整合了图之间的结构和属性相关性。 为了建立直觉，我们首先分析了相关联的高斯混合模型，在该模型中只有相关联的节点属性可用而没有边，并确定了使属性最小化距离的估计器实现两个数据库之间节点精确匹配的条件。 对于相关联的CSBM，我们开发了一种两步程序，首先利用边信息对大多数节点应用$k$-核心匹配，然后通过基于距离的估计器利用剩余未匹配节点的属性来细化匹配。 我们确定了算法恢复精确节点对应关系的条件，这使得我们可以合并相关的边并平均相关的属性以增强社区检测。 至关重要的是，通过对齐和组合图，我们确定了在单一图中无法实现社区检测但在结合相关图的侧面信息时变得可行的区域。 我们的结果显示了图匹配与社区恢复之间的相互作用如何提高性能，从而扩大了基于多图和属性的社区检测的范围。 显示英文摘要

摘要： We study community detection in multiple networks whose nodes and edges are jointly correlated. This setting arises naturally in applications such as social platforms, where a shared set of users may exhibit both correlated friendship patterns and correlated attributes across different platforms. Extending the classical Stochastic Block Model (SBM) and its contextual counterpart (CSBM), we introduce the correlated CSBM, which incorporates structural and attribute correlations across graphs. To build intuition, we first analyze correlated Gaussian Mixture Models, wherein only correlated node attributes are available without edges, and identify the conditions under which an estimator minimizing the distance between attributes achieves exact matching of nodes across the two databases. For correlated CSBMs, we develop a two-step procedure that first applies $k$-core matching to most nodes using edge information, then refines the matching for the remaining unmatched nodes by leveraging their attributes with a distance-based estimator. We identify the conditions under which the algorithm recovers the exact node correspondence, enabling us to merge the correlated edges and average the correlated attributes for enhanced community detection. Crucially, by aligning and combining graphs, we identify regimes in which community detection is impossible in a single graph but becomes feasible when side information from correlated graphs is incorporated. Our results illustrate how the interplay between graph matching and community recovery can boost performance, broadening the scope of multi-graph, attribute-based community detection.