Analysis of the topological architecture of functional networks

To examine system topology, we calculated within- and cross-system connectivity from the same weighted adjacency matrix as above. Within-system connectivity is the mean strength of the functional interactions within a system (e.g., mean of all connections among DMN nodes). Cross-system connectivity of two systems is the mean strength of functional interactions between ROIs of one system (e.g., DMN) and ROIs of another system (e.g., Salience). Here, the Fisher’s z adjacency matrix is divided by each individual’s global mean Fisher’s z to maximize sensitivity to topological structure and account for individual differences in mean connectivity strength (see additional figures for distribution of mean connectivity strength pre- and post-normalization [Additional file 2]). This approach has been used in a large-scale study of typical development [32], and in a prior study of whole-brain topology in ASD [3]. Normalized correlations are ideally suited for interrogating the topological architecture of functional systems because they control for individual differences in the total weight of connections.

We compared the within-system and cross-system functional connectivity of all normalized systems for ASD and TDC groups while accounting for the major confounding variables of age, IQ, sex, and scan sequence. All within-system and cross-system differences were corrected with a False Discovery Rate (FDR; q < 0.05) on the effect of group in the ANCOVA model while accounting for the number of comparisons for each type of analysis (i.e., 12 for within-system and 66 for cross-system). For each within-system (or cross-system) connection that differed between groups, we examined the relationship with ASD symptoms using raw and calibrated severity scores from the ADOS.