  We study the influence of network topology and connectivity on the
synchronization properties of chaotic logistic maps, interacting with random
delay times. Four different types of topologies are investigated: two regular
(a ring-type and a ring-type with a central node) and two random (free-scale
Barabasi-Albert and small-world Newman-Watts). The influence of the network
connectivity is studied by varying the average number of links per node, while
keeping constant the total input that each map receives from its neighbors. For
weak coupling the array does not synchronize regardless the topology or
connectivity of the network; however, for certain connectivity values there is
enhanced coherence. For strong coupling the array synchronizes in the
homogeneous steady-state, where the chaotic dynamics of the individual maps is
suppressed. For both, weak and strong coupling, the array propensity for
synchronization is largely independent of the network topology and depends
mainly on the average number of links per node.
