  The topology of the Internet has typically been measured by sampling
traceroutes, which are roughly shortest paths from sources to destinations. The
resulting measurements have been used to infer that the Internet's degree
distribution is scale-free; however, many of these measurements have relied on
sampling traceroutes from a small number of sources. It was recently argued
that sampling in this way can introduce a fundamental bias in the degree
distribution, for instance, causing random (Erdos-Renyi) graphs to appear to
have power law degree distributions. We explain this phenomenon analytically
using differential equations to model the growth of a breadth-first tree in a
random graph G(n,p=c/n) of average degree c, and show that sampling from a
single source gives an apparent power law degree distribution P(k) ~ 1/k for k
< c.
