Statistics Department, University of Ghana, Box LG 115, Legon, Ghana. [email protected]
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 H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical measures.
(Received June 19 2009)
(Revised March 31 2010)
(Revised June 9 2010)
(Online publication July 3 2012)
Mathematics Subject Classification: