  Many real-world complex networks arise as a result of a competition between
growth and rewiring processes. Usually the initial part of the evolution is
dominated by growth while the later one rather by rewiring. The initial growth
allows the network to reach a certain size while rewiring to optimise its
function and topology. As a model example we consider tree networks which first
grow in a stochastic process of node attachment and then age in a stochastic
process of local topology changes. The ageing is implemented as a Markov
process that preserves the node-degree distribution. We quantify differences
between the initial and aged network topologies and study the dynamics of the
evolution. We implement two versions of the ageing dynamics. One is based on
reshuffling of leaves and the other on reshuffling of branches. The latter one
generates much faster ageing due to non-local nature of changes.
