  We investigate the influence of morphology and size on the vibrational
properties of disordered clusters of colloidal particles with attractive
interactions. From measurements of displacement correlations between particles
in each cluster, we extract vibrational properties of the corresponding
"shadow" glassy cluster, with the same geometric configuration and interactions
as the "source" cluster but without damping. Spectral features of the
vibrational modes are found to depend strongly on the average number of nearest
neighbors, $\bar{NN}$, but only weakly on the number of particles in each
glassy cluster. In particular, the median phonon frequency, $\omega_{med}$, is
essentially constant for $\bar{NN}$ $<2$ and then grows linearly with
$\bar{NN}$ for $\bar{NN}$ $>2$. This behavior parallels concurrent observations
about local isostatic structures, which are absent in clusters with $\bar{NN}$
$<2$ and then grow linearly in number for $\bar{NN}$$>2$. Thus, cluster
vibrational properties appear to be strongly connected to cluster mechanical
stability (i.e., fraction of locally isostatic regions), and the scaling of
$\omega_{med}$ with $\bar{NN}$ is reminiscent of the behavior of packings of
spheres with repulsive interactions at the jamming transition. Simulations of
random networks of springs corroborate observations and suggest that
connections between phonon spectra and nearest neighbor number are generic to
disordered networks.
