2015/01/12 by Balázs Szalkai, Balazs Szalkai, Bálint Varga +2 · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Neuroscience · #Advanced MRI Techniques and Applications #Advanced Neuroimaging Techniques and Applications #Algorithm #Biology #Bisection #Centrality #Combinatorics #Computer science #Connectome #Connectomics #Data science #Functional Brain Connectivity Studies #Functional connectivity #Graph #Human Connectome Project #Mathematics #Neuroscience #PageRank #Theoretical computer science #Vertex (graph theory) #q-bio.NC
paper · pdf · doi:10.1371/journal.pone.0130045
arxiv created 2015/01/12 · openalex publication_date 2015/07/01 · arxiv updated 2016/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.