One of the defining properties of small worlds is the prevalence of
short paths connecting node pairs. Unfortunately, as a result the usual
notion of distance is not particularly helpful in distinguishing
neighborhoods in such graphs.
We describe a motivating problem that requires a finer-grained notion of
distance. The problem is quite simple to state: how can any given
network operator in the Internet determine which paths pass through its
network? Surprisingly, the nature of Internet routing makes this