Synchronization versus neighborhood similarity in complex networks of nonidentical oscillators

Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of nonidentical interacting oscillators. Three types of connection configurations are considered: Similar, Dissimilar, and Neutral patterns. These different groups correspond, respectively, to oscillators alike, distinct, and indifferent relative to their neighbors. To construct such scenarios we define a vertex-weighted graph measure, the total dissonance, which comprises the sum of the dissonances between all neighbor oscillators in the network. Our numerical simulations show that the more homogeneous a network, the higher tend to be both the coupling strength required for phase locking and the associated final phase configuration spread over the circle. On the other hand, the initial spread of partial synchronization occurs faster for Similar patterns in comparison to Dissimilar ones, while neutral patterns are an intermediate situation between both extremes.