Modeling Topological Impact on Node Attribute Distributions in Attributed Graphs
This work addresses the interaction between topology and attributes in attributed graphs, which is an incremental contribution to graph representation learning.
The paper tackles the problem of how graph topology influences node attribute distributions by introducing an algebraic approach that integrates topology with attribute probability distributions, resulting in topology-influenced distributions, and evaluates it using an unsupervised graph anomaly detection task.
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.