  We present the interplay between synchronization of unidirectional coupled
chaotic nodes with heterogeneous delays and the greatest common divisor (GCD)
of loops composing the oriented graph. In the weak chaos region and for GCD=1
the network is in chaotic zero-lag synchronization, whereas for GCD=m>1
synchronization of m-sublattices emerges. Complete synchronization can be
achieved when all chaotic nodes are influenced by an identical set of delays
and in particular for the limiting case of homogeneous delays. Results are
supported by simulations of chaotic systems, self-consistent and mixing
arguments, as well as analytical solutions of Bernoulli maps.
