Graph theoretic analysis of human brain networks

The human brain is a highly interconnected network. It is thus suitable for investigation with graph theory, a branch of mathematics concerned with understanding systems of interacting elements. Graph theory has become a popular tool for analyzing human MRI data. In this work, brain networks are modeled as graphs of nodes connected by edges. The nodes represent distinct brain regions and the edges represent some measure of structural or functional interaction between regions. This representation enables the computation of a broad range of metrics that quantify diverse aspects of network organization, thus offering a powerful framework for understanding brain structure and function in both health and disease. This chapter overviews the principles and methods involved in building and analyzing graph theoretic models of the brain using MRI. It explains basic concepts, provides examples of how graph theory has shed new light on brain organization, and considers some limitations of current applications.