Generative Modelling of Structurally Constrained Graphs

TL;DR

ConStruct is a new framework that integrates hard structural constraints into graph diffusion models, ensuring generated graphs meet domain-specific properties like planarity or acyclicity, thus improving validity in real-world applications.

Contribution

It introduces an edge-absorbing noise model and projector operator to enforce structural constraints during graph generation, advancing the state-of-the-art in constrained graph diffusion modeling.

Findings

Achieves state-of-the-art performance on synthetic and real datasets.

Improves data validity by up to 71.1 percentage points with constraints.

Demonstrates versatility across various structural constraints.

Abstract

Graph diffusion models have emerged as state-of-the-art techniques in graph generation; yet, integrating domain knowledge into these models remains challenging. Domain knowledge is particularly important in real-world scenarios, where invalid generated graphs hinder deployment in practical applications. Unconstrained and conditioned graph diffusion models fail to guarantee such domain-specific structural properties. We present ConStruct, a novel framework that enables graph diffusion models to incorporate hard constraints on specific properties, such as planarity or acyclicity. Our approach ensures that the sampled graphs remain within the domain of graphs that satisfy the specified property throughout the entire trajectory in both the forward and reverse processes. This is achieved by introducing an edge-absorbing noise model and a new projector operator. ConStruct demonstrates versatility across several structural and edge-deletion invariant constraints and achieves state-of-the-art performance for both synthetic benchmarks and attributed real-world datasets. For example, by incorporating planarity constraints in digital pathology graph datasets, the proposed method outperforms existing baselines, improving data validity by up to 71.1 percentage points.