  Many transport processes on networks depend crucially on the underlying
network geometry, although the exact relationship between the structure of the
network and the properties of transport processes remain elusive. In this paper
we address this question by using numerical models in which both structure and
dynamics are controlled systematically. We consider the traffic of information
packets that include driving, searching and queuing. We present the results of
extensive simulations on two classes of networks; a correlated cyclic
scale-free network and an uncorrelated homogeneous weakly clustered network. By
measuring different dynamical variables in the free flow regime we show how the
global statistical properties of the transport are related to the temporal
fluctuations at individual nodes (the traffic noise) and the links (the traffic
flow). We then demonstrate that these two network classes appear as
representative topologies for optimal traffic flow in the regimes of low
density and high density traffic, respectively. We also determine statistical
indicators of the pre-jamming regime on different network geometries and
discuss the role of queuing and dynamical betweenness for the traffic
congestion. The transition to the jammed traffic regime at a critical posting
rate on different network topologies is studied as a phase transition with an
appropriate order parameter. We also address several open theoretical problems
related to the network dynamics.
