  We present a link rewiring mechanism to produce surrogates of a network where
both the degree distribution and the rich--club connectivity are preserved. We
consider three real networks, the AS--Internet, the protein interaction and the
scientific collaboration. We show that for a given degree distribution, the
rich--club connectivity is sensitive to the degree--degree correlation, and on
the other hand the degree--degree correlation is constrained by the rich--club
connectivity. In particular, in the case of the Internet, the assortative
coefficient is always negative and a minor change in its value can reverse the
network's rich--club structure completely; while fixing the degree distribution
and the rich--club connectivity restricts the assortative coefficient to such a
narrow range, that a reasonable model of the Internet can be produced by
considering mainly the degree distribution and the rich--club connectivity. We
also comment on the suitability of using the maximal random network as a null
model to assess the rich--club connectivity in real networks.
