Topology-aware Graph Diffusion Model with Persistent Homology

Donghyun Lee (Pohang University of Science and Technology) · Guorong Wu (University of North Carolina, Chapel Hill) · Won Hwa Kim (POSTECH) · Joonhyuk Park (Pohang University of Science and Technology) · Yujee Song (Pohang University of Science and Technology)

brain network dataconnected componentsdenoising networkembedding spacegraph benchmarksgraph generationhomological characteristicsjoint distributionloopspdm losspersistence diagram matchingstructural characteristicstopological propertiestopology-aware attention moduletopology-aware diffusion-based graph generation

Generating realistic graphs faces challenges in estimating accurate distribution of graphs in an embedding space while preserving structural characteristics. However, existing graph generation methods primarily focus on approximating the joint distribution of nodes and edges, often overlooking topological properties such as connected components and loops, hindering accurate representation of global structures. To address this issue, we propose a Topology-Aware diffusion-based Graph Generation (TAGG), which aims to sample synthetic graphs that closely resemble the structural characteristics of the original graph based on persistent homology. Specifically, we suggest two core components: 1) Persistence Diagram Matching (PDM) loss which ensures high topological fidelity of generated graphs, and 2) topology-aware attention module (TAM) which induces the denoising network to capture the homological characteristics of the original graphs. Extensive experiments on conventional graph benchmarks demonstrate the effectiveness of our approach demonstrating high generation performance across various metrics, while achieving closer alignment with the distribution of topological features observed in the original graphs. Furthermore, application to real brain network data showcases its potential for complex and real graph applications.