GRAPH THEORY APPLICATIONS IN PROTEIN - PROTEIN INTERACTION NETWORKS

Abstract

Understanding the intricate web of protein–protein interactions (PPIs) is fundamental to decoding cellular behavior and identifying key molecular mechanisms underlying health and disease. This study explores the application of graph theory as a mathematical framework for modeling, simulating, and analyzing Protein–Protein Interaction (PPI) networks. In the proposed methodology, proteins are represented as nodes and interactions as edges, forming a complex, scale-free, and small-world network structure. The study utilizes the Barabási–Albert model to simulate a realistic PPI network, and applies centrality measures such as degree, betweenness, and closeness centrality to identify hub and bottleneck proteins, which play pivotal roles in maintaining network stability and functionality. The simulation and visualization are implemented using Python’s NetworkX library, providing insights into the network’s topological and statistical properties, including clustering coefficient, average path length, and degree distribution. The results reveal a characteristic power-law degree distribution, confirming the presence of hub proteins and the robust yet fragile nature of biological networks—robust against random failures but vulnerable to targeted attacks on key nodes. The analysis further demonstrates how community detection and clustering can identify functionally related protein modules, offering valuable biological interpretations. This graph-theoretic approach bridges computational mathematics and molecular biology, providing a quantitative and scalable framework for understanding complex biological systems, predicting essential proteins, and supporting drug discovery efforts.