  We address the problem of link reciprocity, the non-random presence of two
mutual links between pairs of vertices. We propose a new measure of reciprocity
that allows the ordering of networks according to their actual degree of
correlation between mutual links. We find that real networks are always either
correlated or anticorrelated, and that networks of the same type (economic,
social, cellular, financial, ecological, etc.) display similar values of the
reciprocity. The observed patterns are not reproduced by current models. This
leads us to introduce a more general framework where mutual links occur with a
conditional connection probability. In some of the studied networks we discuss
the form of the conditional connection probability and the size dependence of
the reciprocity.
