Concepts and principles in the analysis of brain networks

The brain is a large-scale network, operating at multiple levels of information processing ranging from neurons, to local circuits, to systems of brain areas. Recent advances in the mathematics of graph theory have provided tools with which to study networks. These tools can be employed to understand how the brain's behavioral repertoire is mediated by the interactions of objects of information processing. Within the graph-theoretic framework, networks are defined by independent objects (nodes) and the relationships shared between them (edges). Importantly, the accurate incorporation of graph theory into the study of brain networks mandates careful consideration of the assumptions, constraints, and principles of both the mathematics and the underlying neurobiology. This review focuses on understanding these principles and how they guide what constitutes a brain network and its elements, specifically focusing on resting-state correlations in humans. We argue that approaches that fail to take the principles of graph theory into consideration and do not reflect the underlying neurobiological properties of the brain will likely mischaracterize brain network structure and function.