  We use mathematical methods from the theory of tailored random graphs to
study systematically the effects of sampling on topological features of large
biological signalling networks. Our aim in doing so is to increase our
quantitative understanding of the relation between true biological networks and
the imperfect and often biased samples of these networks that are reported in
public data repositories and used by biomedical scientists. We derive exact
explicit formulae for degree distributions and degree correlation kernels of
sampled networks, in terms of the degree distributions and degree correlation
kernels of the underlying true network, for a broad family of sampling
protocols that include (un-)biased node and/or link undersampling as well as
(un-)biased link oversampling. Our predictions are in excellent agreement with
numerical simulations.
