Sampling of Networks with Traceroute-Like Probes

A large part of the recent development of the interest in complex networks has been triggered by the observation of particular characteristics of real world networks, such as the small-world properties or the heavy-tailed distributions of degrees. Many datasets are, however, the result of an incomplete sampling of the underlying real networks, and it has been argued that sampling procedures might introduce uncontrolled biases in the statistical properties of the sampled graph. In this paper, we explore this issue in the case of the Internet, which is generally mapped from a limited set of sources by using traceroute-like probes. The origin of the biases introduced by such a sampling process is investigated and related with the global topological properties of the underlying network. We complement the analytical discussion with a thorough numerical investigation of simulated mapping strategies in network models with different topologies.