ωiis the angular velocity of the i-th oscillator and is the couplingstrength and dij is the connectivity matrix with values of 1 if the i-th and j-th node are connectedand 0 otherwise. Angular velocities ωi were distributed according to a normal distribution withmean angular velocity ω = 1.0 with standard deviation of 0.2. The limit cycle radius was set toA = 1.0 and the coupling strength to = 0.25.The parameter γ determines the relaxation towards the limit cycle and is immediately relatedwith the dissipation rate of the oscillators [5, 8]. In order to investigate the interplay betweenstructural and dynamical features of the network, we simulated how the overall synchronizationin the systems changes according to the initial rigidity of the oscillators and structural propertiesof the network. For that purpose we analyze the synchronization behavior as a function ofthe relaxation rate γ and network topology parameter δ. For the quantification of the globalnetwork synchronization we calculate the average correlation coefficient R. Accordingly, we haveto construct the N × N correlation matrix, whose ij-th element is defined as