The topology of large Open Connectome networks for the human brain

TL;DR

This paper analyzes large human brain connectome networks, revealing that their degree distributions are best described by a generalized Weibull distribution and that their topology is predominantly low-dimensional with small-world features.

Contribution

It provides a detailed statistical and topological analysis of large-scale human brain networks, highlighting the suitability of the Weibull distribution and low-dimensional topology.

Findings

Degree distributions fit a generalized Weibull distribution.

Networks exhibit small-world properties with low topological dimension.

Long-distance connections only slightly increase the network's topological dimension.

Abstract

The structural human connectome (i.e.\ the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging. Here we analyze several large data sets for the human brain network made available by the Open Connectome Project. We apply statistical model selection to characterize the degree distributions of graphs containing up to $\simeq 10^6$ nodes and $\simeq 10^8$ edges. A three-parameter generalized Weibull (also known as a stretched exponential) distribution is a good fit to most of the observed degree distributions. For almost all networks, simple power laws cannot fit the data, but in some cases there is statistical support for power laws with an exponential cutoff. We also calculate the topological (graph) dimension $D$ and the small-world coefficient $\sigma$ of these networks. While $\sigma$ suggests a small-world topology, we found that $D < 4$ showing that long-distance connections provide only a small correction to the topology of the embedding three-dimensional space.