  We quantify the dynamical implications of the small-world phenomenon. We
consider the generic synchronization of oscillator networks of arbitrary
topology, and link the linear stability of the synchronous state to an
algebraic condition of the Laplacian of the graph. We show numerically that the
addition of random shortcuts produces improved network synchronizability.
Further, we use a perturbation analysis to place the synchronization threshold
in relation to the boundaries of the small-world region. Our results also show
that small-worlds synchronize as efficiently as random graphs and hypercubes,
and more so than standard constructive graphs.
