Modeling Topological Impact on Node Attribute Distributions in Attributed Graphs

2026-02-01

AI Summary

This study investigates how graph topology influences the distribution of node attributes in attributed graphs. To this end, the authors propose an algebraic framework grounded in category theory to formally model how nodes perceive graph topology and to construct a probabilistic model of attribute distributions conditioned on topological structure. The model is theoretically sound, as it recovers the original attribute distribution in the limiting case of a complete graph. By integrating category theory, probabilistic modeling, and algebraic graph methods, the work achieves a unified representation of topology-aware attribute distributions. Empirical evaluation through unsupervised graph anomaly detection on a custom ID testing benchmark demonstrates that the proposed approach effectively captures the structural influence of topology on attribute distributions.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

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.

Problem

• attributed graphs
• topology
• node attribute distributions
• graph structure
• topological influence

Innovation

• attributed graphs
• topological influence
• categorical framework
• topology-conditioned distribution
• graph anomaly detection