Alternate Depictions of Internet Routes
I was curious what could be learned regarding the gross structure of the internet by tracing routes to a collection of IP addresses. While hardly a broad systematic exploration, it still yielded an interesting dataset. These views present the same network information in two distinct forms. They depict the path to a few hundred endpoints and about 1300 routers encountered along the way.
Combined View

The logical graph clearly illustrates that traces originated from a single root node (my computer) and were generally depth-first to relatively distant nodes. This is evidenced by a sparse branching structure except near the center. One could easily discover branches at nearly any level within a route and thereby construct a far denser graph if that was the goal. It's also possible to trace routes from different starting points, but the resulting graph would be far more complex as it would no longer be a tree with a single root node.
Individual Visualizations
The combined view above is a far better tool for exploration. These individual views are recommended only if the combined view does not perform well (in which case you must be using a very old browser or computer), or if you want to read notes about that particular visualization.Geographic View

Logical Graph View

Each individual view contains an explanation with some detail about the tools and methodology.