# Principal Interconnections of the Human Brain

The Stanford GraphBase has a small collection of graphs that are used (or planned to be used) in examples of The Art of Computer Programming. One of these sample graphs, brain83.gb, models the major interconnections between 83 basic brain areas called ROIs (“Regions Of Interest”).

This graph contains 83 vertices, one for each principal ROI. If v points to such a vertex, its name v->name has the form ‘letter hyphen ROIname’. For example, g->vertices->name, the name of vertex 0, is B-Stem because it represents the brain stem. The initial letter of other vertex names is either l or r for cortical ROIs, either L or R for subcortical ROIs, on the left or right respectively.

Besides its name, each vertex v also has three utility fields v->x.I, v->y.I, v->z.I, giving approximate coordinates. The x coordinate is zero for the brain stem, negative for the left brain, and positive for the right brain. If k is between 0 and 40, vertices 1+k and 42+k are corresponding ROIs on the right and the left. Their y and z coordinates are approximately equal, and their x coordinates are approximately negatives of each other.

The graph has 1654 edges, each of which has a nonnegative length. These lengths are logarithmic: Length l actually stands for a weight proportional to Exp(-l/1000). The three shortest lengths, which represent the strongest interconnections, are: 0 (between r-superiorparietal and r-precuneous); 6 (between l-superiorparietal and l-precuneous); 33 (between L-Caudate and R-Caudate). The longest length is 1336 (between r-superiorparietal and R-Accumbens-area).

One can easily work with a subset of edges, by restricting attention to arcs of small length. For instance, to get roughly 1/4 or 1/2 or 3/4 of the edges, you can simply ignore arcs whose length is greater than 441 or 704 or 981, respectively.

This data is based on the scans of 423 brains by the Human Connectome Project, which of course resulted in Big Data with much greater resolution. [See Kerepesi, Szalkai, Varga, and Grolmusz, Cognitive Neurodynamics 11 (2017), 483–486.] Alain Goriely gave me his simplified combination of that scan data, with self-loops removed and with weights obtained by averaging ‘number-of-fibers/length-of-fibers’. Then I rounded everything down to relatively small numbers.

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