Human structural and functional brain architecture is increasingly studied by applying the mathematical framework of complex networks to data from magnetic resonance imaging. Connections (edges) in such brain networks are commonly constructed using correlations of features between pairs of brain regions, such as regional morphology (across participants) or neurophysiological time series (within participants). Subsequent analyses frequently focus on summary network statistics calculated using the strongest correlations, but often neglect potential underlying shifts within the correlation distribution. This thesis presents methods for the construction and analysis of correlation-derived structural and functional brain networks, focusing on the implications of changes within the correlation distribution.

First, schizophrenia is considered as an example disease which is known to present a reduction in mean correlation between regional neurophysiological time series. Previous studies reported increased network randomisation in schizophrenia, but these results may have been driven by inclusion of a greater number of noisy edges in patients’ networks, based on retention of a fixed proportion of the strongest edges during network thresholding. Here, a novel probabilistic thresholding procedure is applied, based on the realisation that the strongest edges are not necessarily most likely to be true following adjustment of edge probabilities for effects of participant in-scanner motion. Probabilistically thresholded functional networks show decreased randomness, and increased consistency across participants. Further, applying probabilistic thresholding eliminates increased network randomisation in schizophrenia, supporting the hypothesis that previously reported group differences originated in the application of standard thresholding approaches to patient networks with decreased functional correlations.

Subsequently, healthy adolescent development is studied, to help understand the frequent emergence of psychiatric disorders in this period. Importantly, both structural and functional brain networks undergo maturational shifts in correlation distribution over adolescence. Due to reliance of structural correlation networks on a group of subjects, previous studies of adolescent structural network development divided groups into discrete age-bins. Here, a novel sliding-window method is used to describe adolescent development of structural correlation networks in a continuous manner. Moreover, networks are probabilistically thresholded by retaining edges that are most consistent across bootstrapped samples of participants, leading to clearer maturational trajectories. These structural networks show non-linear trajectories of adolescent development driven by changes in association cortical areas, compatible with a developmental process of pruning combined with consolidation of surviving connections. Robustness of the results is demonstrated using extensive sensitivity analyses.

Finally, adolescent developmental changes in functional network architecture are described, focusing on the characterisation of unthresholded (fully weighted) networks. The distribution of functional correlations presents a non-uniform shift over adolescence. Initially strong cortical connections to primary sensorimotor areas further strengthen into adulthood, whereas association cortical and subcortical edges undergo a subtler reorganisation of functional connectivity. Furthermore, individual subcortical regions show distinct maturational profiles. Patterning of maturation according to known functional systems is affirmed by partitioning regions developing at similar rates into maturational modules.

Taken together, this thesis comprises novel methods for the characterisation of disease-related and normative developmental changes in structural and functional correlation brain networks. These methods are generalizable to a wide range of scenarios, beyond the specific disease and developmental age-ranges presented herein.