  Internet mapping projects generally consist in sampling the network from a
limited set of sources by using traceroute probes. This methodology, akin to
the merging of spanning trees from the different sources to a set of
destinations, leads necessarily to a partial, incomplete map of the Internet.
Accordingly, determination of Internet topology characteristics from such
sampled maps is in part a problem of statistical inference. Our contribution
begins with the observation that the inference of many of the most basic
topological quantities -- including network size and degree characteristics --
from traceroute measurements is in fact a version of the so-called `species
problem' in statistics. This observation has important implications, since
species problems are often quite challenging. We focus here on the most
fundamental example of a traceroute internet species: the number of nodes in a
network. Specifically, we characterize the difficulty of estimating this
quantity through a set of analytical arguments, we use statistical subsampling
principles to derive two proposed estimators, and we illustrate the performance
of these estimators on networks with various topological characteristics.
