Recent years have witnessed a surge in the application of graph theory to complex biological systems. The ability of graph theory to extract essential knowledge from the plethora of information embedded in a complex system has proven rewarding in many disciplines ranging from evolutionary biology to cancer prediction. The modular structure of complex networks, a branch of graph theory, is the focus of this text. Its guiding hypothesis, derived from statistical physics, states that modularity correlates with performances of complex biological systems and that the direction of correlation is mediated by environmental stress. This text tests and expands the theory of modularity in three main contexts - gene co-expression networks, human brain networks, and genome-scale metabolic networks. It is demonstrated that modularity of cancer-associated gene co-expression network is predictive of cancer aggressiveness, that modularity of resting-state functional connectivity in healthy young adults correlates with cognitive performance and the correlation is mediated by task complexity, and that modularity of human brain metabolic network not only predicts risk for Alzheimer’s disease but also defines the brain regions where metabolism correlates with dementia-risk gene expression. In addition, definition of modularity and maximization algorithm for bipartite, directed, and weighted networks are proposed and subsequently tested on a genome-scale bacterial metabolic network under different levels of survival stress.

Overall, results presented here support the hypothesis of modularity’s role as a performance predictor for complex systems. The existing theory of modularity has been validated in numerous scenarios and expanded with the concept of ”network fragmentation”. Modularity can be applied to clinical settings for risk evaluation, and even contribute to individualized therapy. It can also help understand the mechanism of biological processes that are currently poorly understood. Of course, future research is needed to further the understanding of the emergence of modularity in complex systems and its application. Better definition of modularity, faster and more functionally appropriate clustering algorithm, and the collection of larger amount of higher quality data are crucial for the advancement of the field.