Null models in network neuroscience

Recent advances in imaging and tracing technology provide increasingly detailed reconstructions of brain connectomes. Concomitant analytic advances enable rigorous identification and quantification of functionally important features of brain network architecture. Null models are a flexible tool to statistically benchmark the presence or magnitude of features of interest, by selectively preserving specific architectural properties of brain networks while systematically randomizing others. Here we describe the logic, implementation and interpretation of null models of connectomes. We introduce randomization and generative approaches to constructing null networks, and outline a taxonomy of network methods for statistical inference. We highlight the spectrum of null models - from liberal models that control few network properties, to conservative models that recapitulate multiple properties of empirical networks - that allow us to operationalize and test detailed hypotheses about the structure and function of brain networks. We review emerging scenarios for the application of null models in network neuroscience, including for spatially embedded networks, annotated networks and correlation-derived networks. Finally, we consider the limits of null models, as well as outstanding questions for the field.