  Small world networks interpolate between fully regular and fully random
topologies and simultaneously exhibit large local clustering as well as short
average path length. Small world topology has therefore been suggested to
support network synchronization. Here we study the asymptotic speed of
synchronization of coupled oscillators in dependence on the degree of
randomness of their interaction topology in generalized Watts-Strogatz
ensembles. We find that networks with fixed in-degree synchronize faster the
more random they are, with small worlds just appearing as an intermediate case.
For any generic network ensemble, if synchronization speed is at all extremal
at intermediate randomness, it is slowest in the small world regime. This
phenomenon occurs for various types of oscillators, intrinsic dynamics and
coupling schemes.
