  We prove asymptotic equipartition properties for simple hierarchical
structures (modelled as multitype Galton-Watson trees) and networked structures
(modelled as randomly coloured random graphs). For example, for large $n$, a
networked data structure consisting of $n$ units connected by an average number
of links of order $n/log n$ can be coded by about $nH$ bits, where $H$ is an
explicitly defined entropy. The main technique in our proofs are large
deviation principles for suitably defined empirical measures.
