  The correlations of several fundamental properties of human brain connections
are investigated in a consensus connectome, constructed from 1064 braingraphs,
each on 1015 vertices, corresponding to 1015 anatomical brain areas. The
properties examined include the edge length, the fiber number, or edge width,
meaning the number of discovered axon bundles forming the edge and the
occurrence number of the edge, meaning the number of individual braingraphs
where the edge exists. By using our previously published robust braingraphs at
\url{https://braingraph.org}, we have prepared a single consensus graph from
the data and compared the statistical similarity of the edge occurrence
numbers, edge lengths, and fiber counts of the edges. We have found a strong
positive Spearman correlation between the edge occurrence numbers and the fiber
count numbers, showing that statistically, the most frequent cerebral
connections have the largest widths, i.e., the fiber number. We have found a
negative Spearman correlation between the fiber lengths and fiber counts,
showing that, typically, the shortest edges are the widest or strongest by
their fiber counts. We have also found a negative Spearman correlation between
the occurrence numbers and the edge lengths: it shows that typically, the long
edges are infrequent, and the frequent edges are short.
