揭示图结构如何影响节点属性分布，提出数学框架捕捉拓扑作用。
Modeling Topological Impact on Node Attribute Distributions in Attributed Graphs
- 用代数方法将图拓扑与属性分布结合，构建拓扑感知的分布模型。
- 在完全图上验证，拓扑无信息时恢复原始属性分布，证明方法自洽。
- 适用于图异常检测等任务，适合研究图结构与属性关系的学者。
本文研究图结构如何影响属性图中节点属性的分布。提出将拓扑与属性视为结构上独立但相互作用的组件的新视角。引入一种代数方法，将图的拓扑与节点属性的概率分布结合，生成受拓扑影响的分布。首先建立范畴论框架，形式化节点对图拓扑的感知方式；进而量化该感知，并与属性分布融合以捕捉拓扑效应。将这些拓扑条件分布解释为后验近似 $P(ullet ext{ }| v)$ 与 $P(ullet ext{ }| ext{G})$。进一步通过理论证明：在完全图（拓扑无信息结构）上，该构造能恢复原始属性分布，建立其合理性。为评估方法，设计一个简单测试模型 $ extbf{ID}$，并以无监督图异常检测作为探测任务。
原文摘要 · Abstract (English)
We investigate how the topology of attributed graphs influences the distribution of node attributes. This work offers a novel perspective by treating topology and attributes as structurally distinct but interacting components. We introduce an algebraic approach that combines a graph's topology with the probability distribution of node attributes, resulting in topology-influenced distributions. First, we develop a categorical framework to formalize how a node perceives the graph's topology. We then quantify this point of view and integrate it with the distribution of node attributes to capture topological effects. We interpret these topology-conditioned distributions as approximations of the posteriors $P(\cdot \mid v)$ and $P(\cdot \mid \mathcal{G})$. We further establish a principled sufficiency condition by showing that, on complete graphs, where topology carries no informative structure, our construction recovers the original attribute distribution. To evaluate our approach, we introduce an intentionally simple testbed model, $\textbf{ID}$, and use unsupervised graph anomaly detection as a probing task.
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