Dynamics of condensation in growing complex networks.

A condensation transition was predicted for growing technological networks evolving by preferential attachment and competing quality of their nodes, as described by the fitness model. When this condensation occurs, a node acquires a finite fraction of all the links of the network. Earlier studies based on steady-state degree distribution and on the mapping to Bose-Einstein condensation were able to identify the critical point. Here we characterize the dynamics of condensation and we present evidence that below the condensation temperature there is a slow down of the dynamics and that a single node (not necessarily the best node in the network) emerges as the winner for very long times. The characteristic time t;{*} at which this phenomenon occurs diverges both at the critical point and at T-->0 when new links are attached deterministically to the highest quality node of the network.