  Partial, instead of complete, synchronization has been widely observed in
various networks including, in particular, brain networks. Motivated by data
from human brain functional networks, in this technical note, we analytically
show that partial synchronization can be induced by strong regional connections
in coupled subnetworks of Kuramoto oscillators. To quantify the required
strength of regional connections, we first obtain a critical value for the
algebraic connectivity of the corresponding subnetwork using the incremental 2
norm. We then introduce the concept of the generalized complement graph, and
obtain another condition on the weighted nodal degree by using the incremental
infinity norm. Under these two conditions, regions of attraction for partial
phase cohesiveness are estimated in the forms of the incremental 2 and infinity
norms, respectively. Our result based on the incremental infinity norm is the
first known criterion that is applicable to non-complete graphs. Numerical
simulations are performed on a two-level network to illustrate our theoretical
results; more importantly, we use real anatomical brain network data to show
how our results may reveal the interplay between anatomical structure and
empirical patterns of synchrony.
