AI 中文总结
该研究针对现有图划分比较度量忽略图拓扑的问题，提出通过诱导边划分的图感知距离构造方法，开发了信息变异度等图感知版本，在随机块模型下验证其有效性，为图划分比较提供了尊重结构的框架。
AI 中文摘要
比较图划分是网络结构化数据分析的基础，但现有的图划分比较度量通常依赖与图无关的指标，将顶点视为可交换的，忽略了编码社区凝聚与分离关键信息的底层图拓扑结构。我们提出了一种通用的图感知距离构造方法，该方法通过诱导边划分来比较顶点划分，并在连续图划分空间上产生有效度量。作为特例，我们开发了图感知版本的信息变异度、van Dongen距离以及基于二分割的伴随距离，并证明这些距离满足自然的局部图感知细化准则。在随机块模型下，我们证明在社区间和社区内划分场景中，更强的拓扑破坏几乎必然导致渐近更大的距离。这些结果提供了一个简单且原则性的框架，用于在尊重底层图结构的同时比较图划分。
英文摘要
Comparing graph partitions is fundamental to the analysis of network-structured data, yet existing measures for comparing graph partitions typically rely on graph-agnostic indices that treat vertices as exchangeable, ignoring the underlying graph topology that encodes essential information about community cohesion and separation. We propose a general construction of graph-informed distances that compares vertex partitions through induced edge partitions and yields valid metrics on the space of contiguous graph partitions. As special cases, we develop graph-informed versions of variation of information and the van Dongen distance together with a binary cut-based companion distance, and show that these distances satisfy a natural local graph-aware refinement criterion. Under stochastic block models, we prove that stronger topological disruptions incur asymptotically larger distances almost surely in both inter-community and intra-community split settings. These results provide a simple and principled framework to compare graph partitions while respecting the underlying graph structure.
