Graph theory methods: applications in brain networks

Network neuroscience is a thriving and rapidly expanding field. Empirical data on brain networks, from molecular to behavioral scales, are ever increasing in size and complexity. These developments lead to a strong demand for appropriate tools and methods that model and analyze brain network data, such as those provided by graph theory. This brief review surveys some of the most commonly used and neurobiologically insightful graph measures and techniques. Among these, the detection of network communities or modules, and the identification of central network elements that facilitate communication and signal transfer, are particularly salient. A number of emerging trends are the growing use of generative models, dynamic (time-varying) and multilayer networks, as well as the application of algebraic topology. Overall, graph theory methods are centrally important to understanding the architecture, development, and evolution of brain networks.