A Topological Data Analysis Framework for Identifying Critical Nodes in Complex Biological Networks

Abstract

The identification of critical nodes within complex biological networks is a fundamental challenge in systems biology and has profound implications for drug discovery and disease treatment. Traditional methods, primarily based on graph-theoretic centrality measures, often fail to capture the higher-order structural organization inherent in these networks. In this paper, we propose a novel framework based on Topological Data Analysis (TDA), specifically utilizing persistent homology, to identify structurally significant nodes. By representing protein-protein interaction (PPI) networks as simplicial complexes, our method identifies nodes that are critical to maintaining the network's essential topological features, such as loops and voids. We applied our framework to the yeast Saccharomyces cerevisiae PPI network and demonstrated its superior performance in identifying essential proteins compared to standard metrics like degree and betweenness centrality. Our results show that this topological approach provides a more robust and biologically relevant measure of node importance, offering a powerful new tool for network analysis.