Topological Graph Neural Networks: A Novel Approach for Geometric Deep Learning

ABSTRACT This paper introduces a novel approach to graph neural networks (GNNs) that incorporates topological data analysis (TDA) to enhance the representational power of traditional GNN architectures. We propose Topological Graph Neural Networks (TopGNNs), which leverage persistent homology and simplicial complexes to capture multi‐scale structural information that conventional GNNs often overlook. Our experimental results on benchmark datasets demonstrate that TopGNNs achieve competitive performance compared to state‐of‐the‐art methods, particularly for tasks requiring sensitivity to global graph structure. We provide a comprehensive empirical analysis of TopGNNs across various domains including molecular property prediction, social network analysis, and citation networks. The proposed framework bridges the gap between algebraic topology and deep learning on graphs, offering a promising direction for future research in geometric deep learning.