  We discuss two sampling schemes for selecting random subnets from a network:
Random sampling and connectivity dependent sampling, and investigate how the
degree distribution of a node in the network is affected by the two types of
sampling. Here we derive a necessary and sufficient condition that guarantees
that the degree distribution of the subnet and the true network belong to the
same family of probability distributions. For completely random sampling of
nodes we find that this condition is fulfilled by classical random graphs; for
the vast majority of networks this condition will, however, not be met. We
furthermore discuss the case where the probability of sampling a node depends
on the degree of a node and we find that even classical random graphs are no
longer closed under this sampling regime. We conclude by relating the results
to real {\it E.coli} protein interaction network data.
