  The main motivation for this paper is to present a definition of network
synchronizability for the case of cluster synchronization (CS), in an analogous
fashion to Barahona and Pecora for the case of complete synchronization. We
find this problem to be substantially more complex than the original one. We
distinguish between the two cases of networks with intertwined clusters and no
intertwined clusters and between {the two cases that the master stability
function is negative either in a bounded range or in an unbounded range of its
argument. We first obtain a definition of synchronizability that applies to
each individual cluster within a network and then attempt to generalize this
definition to the entire network. For CS, the synchronous solution of each
cluster may be stable independent of the stability of the other clusters, which
results in possibly different ranges in which each cluster synchronizes
(isolated CS.) For each pair of clusters, we distinguish between three
different cases: Matryoshka Cluster Synchronization (when the range of the
stability of the synchronous solution for one cluster is included in that of
the other cluster), Partially Disjoint Cluster Synchronization (when the ranges
of stability of the synchronous solutions partially overlap), and Complete
Disjoint Cluster Synchronization (when the ranges of stability of the
synchronous solutions do not overlap.)
