Extending this discussion, I'm still curious about the best way to describe the structure of the cortex in terms of either graph theory or as a data structure.
From what I know of graph theory, the cortex can best be described as:
1) A directed graph (meaning there is directionality between nodes, in this case the flow of information)
2) Cyclical (the flow of information is not in a uniform direction, but cycles or loops through at least some of the nodes)
In terms of data structure, any given node in the cortex can have:
1) 0, 1, or many peers
2) 0, 1, or many parents
3) 0, 1, or many children
Connections (or edges, using graph theory lingo) can occur between any two nodes in the system. However, there is a strong bias in connectivity: It tends to be local. Which means that while there are long-range connections in the cortex, and connectivity sometimes jumps levels in the hierarchy, the bulk of it is between immediate parents, children, and peers.
There does seem to be a bias toward fan-in as you move up the hierarchy. This means that there tend to be fewer nodes in lower levels of the hierarchy than higher levels (e.g. the primary visual cortex is bigger than the secondary visual cortex). But this again is a bias, not true in all instances.
So is there a word or phrase that best captures this particular kind of structure? Network seems too general and anarchic. You could just say it's a hierarchical network with a bias toward local connectivity. My advisor has used the term lattice or lattice hierarchy. I think those are interesting terms, though I'm not entirely sold on them.