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

Szalkai B, Varga B, Grolmusz V - PLoS ONE (2015)

Bottom Line: 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.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.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.

View Article: PubMed Central - PubMed

Affiliation: PIT Bioinformatics Group, Eötvös University, H-1117 Budapest, Hungary.

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.

No MeSH data available.


Related in: MedlinePlus

Panel A: An X-Y cut. The cut-edges are colored black. Panel B: An un-balanced minimum cut. Panel C: A balanced cut. Panel D: The wheel graph.
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pone.0130045.g001: Panel A: An X-Y cut. The cut-edges are colored black. Panel B: An un-balanced minimum cut. Panel C: A balanced cut. Panel D: The wheel graph.

Mentions: Suppose the nodes, or the vertices, of a graph are partitioned into two, disjoint, non-empty sets, say X and Y; their union is the whole vertex-set of the graph. The X, Ycut is the set of all edges connecting vertices of X with the vertices of Y (Fig 1 panel A). The size of the cut is the number of edges in the cut. In graph theory, the size of the minimum cut is an interesting quantity. The minimum cut between vertices a and b is the minimum cut, taken for all X and Y, where vertex a is in X and b is in Y. This quantity gives the “bottleneck”, in a sense, between those two nodes (c.f., Menger theorems and Ford-Fulkerson’s Min-Cut-Max-Flow theorem [20, 21]). The minimum cut in a graph is defined to be the cut with the fewest edges for all non-empty sets X and Y, partitioning the vertices.


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

Szalkai B, Varga B, Grolmusz V - PLoS ONE (2015)

Panel A: An X-Y cut. The cut-edges are colored black. Panel B: An un-balanced minimum cut. Panel C: A balanced cut. Panel D: The wheel graph.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4488527&req=5

pone.0130045.g001: Panel A: An X-Y cut. The cut-edges are colored black. Panel B: An un-balanced minimum cut. Panel C: A balanced cut. Panel D: The wheel graph.
Mentions: Suppose the nodes, or the vertices, of a graph are partitioned into two, disjoint, non-empty sets, say X and Y; their union is the whole vertex-set of the graph. The X, Ycut is the set of all edges connecting vertices of X with the vertices of Y (Fig 1 panel A). The size of the cut is the number of edges in the cut. In graph theory, the size of the minimum cut is an interesting quantity. The minimum cut between vertices a and b is the minimum cut, taken for all X and Y, where vertex a is in X and b is in Y. This quantity gives the “bottleneck”, in a sense, between those two nodes (c.f., Menger theorems and Ford-Fulkerson’s Min-Cut-Max-Flow theorem [20, 21]). The minimum cut in a graph is defined to be the cut with the fewest edges for all non-empty sets X and Y, partitioning the vertices.

Bottom Line: 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.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.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.

View Article: PubMed Central - PubMed

Affiliation: PIT Bioinformatics Group, Eötvös University, H-1117 Budapest, Hungary.

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.

No MeSH data available.


Related in: MedlinePlus