About connections.

Despite the attention attracted by "connectomics", one can lose sight of the very real questions concerning "What are connections?" In the neuroimaging community, "structural" connectivity is ground truth and underlying constraint on "functional" or "effective" connectivity. It is referenced to underlying anatomy; but, as increasingly remarked, there is a large gap between the wealth of human brain mapping and the relatively scant data on actual anatomical connectivity. Moreover, connections have typically been discussed as "pairwise", point x projecting to point y (or: to points y and z), or more recently, in graph theoretical terms, as "nodes" or regions and the interconnecting "edges". This is a convenient shorthand, but tends not to capture the richness and nuance of basic anatomical properties as identified in the classic tradition of tracer studies. The present short review accordingly revisits connectional weights, heterogeneity, reciprocity, topography, and hierarchical organization, drawing on concrete examples. The emphasis is on presynaptic long-distance connections, motivated by the intention to probe current assumptions and promote discussions about further progress and synthesis.