  Brain areas' functional repertoires are shaped by their incoming and outgoing
structural connections. In empirically measured networks, most connections are
short, reflecting spatial and energetic constraints. Nonetheless, a small
number of connections span long distances, consistent with the notion that the
functionality of these connections must outweigh their cost. While the precise
function of these long-distance connections is not known, the leading
hypothesis is that they act to reduce the topological distance between brain
areas and facilitate efficient interareal communication. However, this
hypothesis implies a non-specificity of long-distance connections that we
contend is unlikely. Instead, we propose that long-distance connections serve
to diversify brain areas' inputs and outputs, thereby promoting complex
dynamics. Through analysis of five interareal network datasets, we show that
long-distance connections play only minor roles in reducing average interareal
topological distance. In contrast, areas' long-distance and short-range
neighbors exhibit marked differences in their connectivity profiles, suggesting
that long-distance connections enhance dissimilarity between regional inputs
and outputs. Next, we show that -- in isolation -- areas' long-distance
connectivity profiles exhibit non-random levels of similarity, suggesting that
the communication pathways formed by long connections exhibit redundancies that
may serve to promote robustness. Finally, we use a linearization of
Wilson-Cowan dynamics to simulate the covariance structure of neural activity
and show that in the absence of long-distance connections, a common measure of
functional diversity decreases. Collectively, our findings suggest that
long-distance connections are necessary for supporting diverse and complex
brain dynamics.
