Dynamical networks with diffusive couplings are investigated from the point of view of synchronizability. Arbitrary connection graphs are admitted but the coupling is symmetric. Networks with equal interaction coefficients for all edges of the interaction graph are compared with networks where the interaction coefficients vary from edge to edge according to the bounds for global synchronization obtained by the connection graph stability method. Synchronizability is tested numerically by establishing the time to decrease the synchronization error from 1 to 10-5 in the case of networks of identical Lorenz or Rössler systems. Synchronizability from the point of view of phase synchronization is also tested for networks of non-identical Lorenz or Rössler systems. In this case the phase-order parameters are compared, as a function of the mean interaction strength. Throughout, as network structures, scale-free and Watts-Strogatz small-world networks are used.