SMapping the Internet  generally consists in  sampling the network from a limited set of probes by using traceroute-like methods, a strategy akin to the merging of different spanning trees to a set of destination. This methodology has been argued to introduce uncontrolled sampling biases that might produce statistical properties of the sampled graph which sharply differ from the original ones.
Here we explore these biases and provide a statistical analysis of their origin. We derive a mean-field analytical approximation for the  probability of edge detection that exploits the role of  the number of probes and targets and allows us to relate the globaltopological properties of the underlying network with the statistical accuracy of the sampled graph. In particular we show that shortest path routed sampling allows a clear discrimination of heavy-tailed underlying graphs.
We complement the analytical discussion with a throughout numerical investigation of simulated mapping strategies in different network models.  We show that sampled graphs provide a fair qualitative characterization of the statistical properties of the original networks in a fair range of different strategies and exploration parameters. The numerical study also allows the identification of intervals of the exploration parameters that optimize the fraction  of nodes and edges discovered in the sampled graph. This finding might hint the steps toward more efficient  mapping  strategies.