  We analyze the synchronization dynamics of phase oscillators far from the
synchronization manifold, including the onset of synchronization on scale-free
networks with low and high clustering coefficients. We use normal coordinates
and corresponding time-averaged velocities derived from the Laplacian matrix,
which reflects the network's topology. In terms of these coordinates,
synchronization manifests itself as a contraction of the dynamics onto
progressively lower-dimensional submanifolds of phase space spanned by
Laplacian eigenvectors with lower eigenvalues. Differences between high and low
clustering networks can be correlated with features of the Laplacian spectrum.
For example, the inhibition of full synchoronization at high clustering is
associated with a group of low-lying modes that fail to lock even at strong
coupling, while the advanced partial synchronizationat low coupling noted
elsewhere is associated with high-eigenvalue modes.
