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Dynamical processes taking place on real networks define on them evolvingsubnetworks whose topology is not necessarily the same of the underlying one.We investigate the problem of determining the emerging degree distribution,focusing on a class of tree-like processes, such as those used to explore theInternet's topology. A general theory based on mean-field arguments isproposed, both for single-source and multiple-source cases, and applied to thespecific example of the traceroute exploration of networks. Our results providea qualitative improvement in the understanding of dynamical sampling and of theinterplay between dynamics and topology in large networks like the Internet.

Dynamic Exploration of Networks: from general principles to the traceroute process