  Diffusion Magnetic Resonance Imaging (MRI) exploits the anisotropic diffusion
of water molecules in the brain to enable the estimation of the brain's
anatomical fiber tracts at a relatively high resolution. In particular,
tractographic methods can be used to generate whole-brain anatomical
connectivity matrix where each element provides an estimate of the connectivity
strength between the corresponding voxels. Structural brain networks are built
using the connectivity information and a predefined brain parcellation, where
the nodes of the network represent the brain regions and the edge weights
capture the connectivity strengths between the corresponding brain regions.
This paper introduces a number of novel scalable methods to generate and
analyze structural brain networks with a varying number of nodes. In
particular, we introduce a new parallel algorithm to quickly generate large
scale connectivity-based parcellations for which voxels in a region possess
highly similar connectivity patterns to the rest of the regions. We show that
the corresponding regional structural consistency is always superior to
randomly generated parcellations over a wide range of parcellation sizes.
Corresponding brain networks with a varying number of nodes are analyzed using
standard graph-theorectic measures, as well as, new measures derived from
spectral graph theory. Our results indicate increasingly more statistical power
of brain networks with larger numbers of nodes and the relatively unique shape
of the spectral profile of large brain networks relative to other well-known
networks.
