  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
non-identical interacting oscillators. Three connection configurations found in
Nature are considered here: Similar, Dissimilar and Neutral patterns. These
strategies correspond respectively to oscillators alike, distinct and
indifferent relate to its 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 is a network, the higher tend to be
both the coupling strength required to 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.
