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

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.

The frequent subgraphs of the connectome of the human brain

“…It is important to note that the number of frequent 1-sets are about the same for all three input sets, the number of frequent length-2 paths are larger for males for 70% and 90% frequencies, while the number of frequent, connected 6-sets are much larger in the case of female connectomes, for all three frequency bounds. This observation independently strengthens our results in [12,4,13], showing that women have "better connected" braingraphs than men.…”

The Frequent Network Neighborhood Mapping of the human hippocampus shows much more frequent neighbor sets in males than in females

“…In a sense, these results show that the neighbor sets of the hippocampus of the women are more varied between individuals, while these sets are more regular, that is, less varied in the case of men's connectomes. These results complement our general studies of the deep graph-theoretical parameters of the connectomes of men and women [5,25,7], where it was proven that women's connectomes are better "connected", in precisely defined mathematical and computer engineering terms.…”

“…While it seems to be clear for all brain scientists that the complex connection patterns of the neurons play a fundamental role in brain function [1,2,3], when the large-scale, macroscopic description of these connections has become available by the development of diffusion MRI techniques, it turned out that novel methods are needed to handle these large graphs [1,2]. MRI-mapped human connectomes have only several hundred or at most one thousand vertices today [4], and, therefore, more complex, more refined graph theoretical algorithms [5,6,7] can be applied for their analysis than the widely followed network science approach, originally developed for tens of millions of vertices of the web graph [8].…”

Comparative connectomics: Mapping the inter-individual variability of connections within the regions of the human brain

“…The braingraphs or connectomes are the well-structured discretizations of the diffusion MRI imaging data that yield new possibilities for the comparison of the connections between distinct brain areas in different subjects [2,3] or for finding common connections in distinct cerebra [4], forming a common, consensus human braingraph.…”