Earlier quoted context omitted.
Sometimes the matrix, like for example the adjacency matrix for Wikipedia internal links, will be very sparse. Another reason to use relations rather than an inefficient, mostly empty implicit data structure. That Wikipedia adjacency matrix would be interesting to visualize, though. There are tools out there for visualizing sparse matrices as graphs: http://yifanhu.net/GALLERY/GRAPHS/
I've never seen a visualization of a graph at the scale of Wikipedia that conveys anything useful in the visualization. You just get a big hairball.
I'd like to see more work like the paper from a few years ago which ran PageRank and HITS on Wikipedia to discover the most central pages. The PageRank result indicated church hierarchy and nation states were important, while HITS had things like "television" "animal" as the most authoritative/central pages.
There is so much structure there to be investigated.