Statistics of weighted brain networks reveal hierarchical organization and Gaussian degree distribution.

Publication Type	Academic Article
Authors	Ivković M, Kuceyeski A, Raj A
Journal	PLoS One
Volume	7
Issue	6
Pagination	e35029
Date Published	06/22/2012
ISSN	1932-6203
Keywords	Brain, Brain Mapping, Cluster Analysis, Models, Statistical, Neural Pathways, Normal Distribution
Abstract	Whole brain weighted connectivity networks were extracted from high resolution diffusion MRI data of 14 healthy volunteers. A statistically robust technique was proposed for the removal of questionable connections. Unlike most previous studies our methods are completely adapted for networks with arbitrary weights. Conventional statistics of these weighted networks were computed and found to be comparable to existing reports. After a robust fitting procedure using multiple parametric distributions it was found that the weighted node degree of our networks is best described by the normal distribution, in contrast to previous reports which have proposed heavy tailed distributions. We show that post-processing of the connectivity weights, such as thresholding, can influence the weighted degree asymptotics. The clustering coefficients were found to be distributed either as gamma or power-law distribution, depending on the formula used. We proposed a new hierarchical graph clustering approach, which revealed that the brain network is divided into a regular base-2 hierarchical tree. Connections within and across this hierarchy were found to be uncommonly ordered. The combined weight of our results supports a hierarchically ordered view of the brain, whose connections have heavy tails, but whose weighted node degrees are comparable.
DOI	10.1371/journal.pone.0035029
PubMed ID	22761649
PubMed Central ID	PMC3382201