# Modeling Topological Impact on Node Attribute Distributions in Attributed Graphs

arXiv: https://arxiv.org/abs/2602.01454 · HTML: https://mlsanity.com/paper/2602.01454/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 1 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [AnomalyDAE: Dual autoencoder for anomaly detection on attributed networks](https://mlsanity.com/paper/2002.03665/) (2020)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [BOND: Benchmarking Unsupervised Outlier Node Detection on Static Attributed Graphs](https://mlsanity.com/paper/2206.10071/) (2022)
- [GAD-NR: Graph Anomaly Detection via Neighborhood Reconstruction](https://mlsanity.com/paper/2306.01951/) (2023)
- [Categorical Foundations of Gradient-Based Learning](https://mlsanity.com/paper/2103.01931/) (2021)
- [Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection](https://mlsanity.com/paper/2306.00006/) (2023)
- [PyGOD: A Python Library for Graph Outlier Detection](https://mlsanity.com/paper/2204.12095/) (2022)
- [Position: Categorical Deep Learning is an Algebraic Theory of All Architectures](https://mlsanity.com/paper/2402.15332/) (2024)
- [Lenses and Learners](https://mlsanity.com/paper/1903.03671/) (2019)
- [Fundamental Components of Deep Learning: A category-theoretic approach](https://mlsanity.com/paper/2403.13001/) (2024)
- [Grothendieck Graph Neural Networks Framework: An Algebraic Platform for Crafting Topology-Aware GNNs](https://mlsanity.com/paper/2412.08835/) (2024)

## Abstract (arXiv)

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(· mid v) and P(· mid 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, ID, and use unsupervised graph anomaly detection as a probing task.