A Topological Approach to Protein-Protein Interaction Networks: Persistent Homology and Algebraic Connectivity

Persistent homology is a powerful tool in topological data analysis that captures the multi-scale topological features of data. In this work, we provide a mathematical introduction to persistent homology and demonstrate its application to protein-protein interaction networks. We combine persistent homology with algebraic connectivity, a graph-theoretic measure of network robustness, to analyze the topology and stability of PPI networks. An example is provided to illustrate the methodology and its potential applications in systems biology.