Graph Theoretical Analysis Reveals: Women's Brains Are Better Connected than Men's.

Balázs Szalkai,Bálint Varga,Vince Grolmusz,Yongtang Shi

doi:10.1371/journal.pone.0130045

Abstract

Deep graph-theoretic ideas in the context with the graph of the World Wide Web led to the definition of Google’s PageRank and the subsequent rise of the most popular search engine to date. Brain graphs, or connectomes, are being widely explored today. We believe that non-trivial graph theoretic concepts, similarly as it happened in the case of the World Wide Web, will lead to discoveries enlightening the structural and also the functional details of the animal and human brains. When scientists examine large networks of tens or hundreds of millions of vertices, only fast algorithms can be applied because of the size constraints. In the case of diffusion MRI-based structural human brain imaging, the effective vertex number of the connectomes, or brain graphs derived from the data is on the scale of several hundred today. That size facilitates applying strict mathematical graph algorithms even for some hard-to-compute (or NP-hard) quantities like vertex cover or balanced minimum cut. In the present work we have examined brain graphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural brain graphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weighs less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections in the brain graph. We have also found that the minimum bisection width, normalized with the edge number, is also significantly larger in the right and the left hemispheres in females: therefore, the differing bisection widths are independent from the difference in the number of edges.

Highlights

In the last several years hundreds of publications appeared describing or analyzing structural or functional networks of the brain, frequently referred to as “connectome” [1,2,3,4]
It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections in the brain graph
We have found that female connectomes have more edges, larger minimum bisection widths, larger minimum-vertex covers and more spanning trees and are better expanders than the male connectomes

Summary

Introduction

In the last several years hundreds of publications appeared describing or analyzing structural or functional networks of the brain, frequently referred to as “connectome” [1,2,3,4]. In the present work we demonstrate that deep and more intricate graph theoretic parameters could be computed by using, among other tools, contemporary integer programming approaches for connectomes with several hundred vertices. With these mathematical tools we show statistically significant differences in some graph properties of the connectomes, computed from MRI imaging data of male and female brains. We clearly demonstrate that deep graph-theoretic parameters show “better” connections in a certain sense in female connectomes than in male ones

Methods

Results

Conclusion