Graph Theory and Modeling of Network Topology in Clinical Neurosurgery

The last several decades have seen a shift in understanding many neurological disorders as abnormalities in brain networks rather than specific brain regions. This conceptual revolution, coupled with advancements in computing capabilities and resources, has enabled a wealth of research on delineating and treating aberrant brain networks. One approach to network neuroscience, graph theory, involves modeling network topologies as mathematical graphs and computing various metrics that describe its characteristics. Using graph theory, researchers have derived new insights into the pathophysiology of many neuropsychiatric disorders and even developed treatments targeted at restoring network disturbances. In this chapter, we provide an overview of the principles of graph theory and how to implement it, specific applications of graph theory within clinical neurosurgery, and a discussion on the advantages and limitations of these approaches.