We employ an adaptive parameter control technique based on detection of phase/lag synchrony between the elements of the system to dynamically modify the structure of a network of nonidentical, coupled Rossler oscillators. Two processes are simulated: adaptation, under which the initially different properties of the units converge, and rewiring, in which clusters of interconnected elements are formed based on the temporal correlations. We show how those processes lead to different network structures and investigate their optimal characteristics from the point of view of resulting network properties.