  Autism is increasing in prevalence and is a neurodevelopmental disorder
characterised by impairments in communication skills and social behaviour.
Connectomes enable a systems-level representation of the brain with recent
interests in understanding the distributed nature of higher order cognitive
function using modules or subnetworks. By dividing the connectome according to
a central component of the brain critical for its function (it's hub), we
investigate network organisation in autism from hub through to peripheral
subnetworks. We complement this analysis by extracting features of energy
transport computed from heat kernels fitted with increasing time steps. This
heat kernel framework is advantageous as it can capture the energy transported
in all direct and indirect pathways between pair-wise regions over 'time', with
features that have correspondence to small-world properties. We apply our
framework to resting-state functional MRI connectomes from a large, publically
available autism dataset, ABIDE. We show that energy propagating through the
brain over time are different between subnetworks, and that heat kernel
features significantly differ between autism and controls. Furthermore, the hub
was functionally preserved and similar to controls, however, increasing
statistical significance between groups was found in increasingly peripheral
subnetworks. Our results support the increasing opinion of non-hub regions
playing an important role in functional organisation. This work shows that
analysing autism by subnetworks with the heat kernel reflects the atypical
activations in peripheral regions as alterations in energy dispersion and may
provide useful features towards understanding the distributed impact of this
disorder on the functional connectome.
