Topological Graph Neural Networks for Drug Repurposing: A Survey of Graph-Theoretic and Mathematical Approaches

Abstract

Drug repurposing has emerged as an efficient approach for identifying new therapeutic uses for
existing drugs, avoiding the time and cost of traditional drug discovery. Biological systems, including
drug–gene and disease–pathway interactions, can be naturally modeled using heterogeneous graphs.
Graph Neural Networks (GNNs) have demonstrated strong capability in learning from such structured
data; however, limited work integrates rigorous mathematical foundations from graph theory and
topology. This paper presents a survey of topological GNN approaches for drug repurposing,
emphasizing spectral graph theory, graph Laplacians, and persistent homology. We categorize existing
models, analyze their mathematical formulations, and evaluate them on benchmark datasets such as
Hetionet and Drug Repurposing Knowledge Graph(DRKG). Key challenges including data sparsity,
interpretability, and generalization are discussed. Finally, we outline future research directions,
including interpretable models and topology-driven feature representations, highlighting the role of
mathematical structures in advancing drug discovery.