  We study the classical and quantum transport processes on some finite
networks and model them by continuous-time random walks (CTRW) and
continuous-time quantum walks (CTQW), respectively. We calculate the classical
and quantum transition probabilities between two nodes of the network. We
numerically show that there is a high probability to find the walker at the
initial node for CTQWs on the underlying networks due to the interference
phenomenon, even for long times. To get global information (independent of the
starting node) about the transport efficiency, we average the return
probability over all nodes of the network. We apply the decay rate and the
asymptotic value of the average of the return probability to evaluate the
transport efficiency. Our numerical results prove that the existence of the
symmetry in the underlying networks makes quantum transport less efficient than
the classical one. In addition, we find that the increasing of the symmetry of
these networks decreases the efficiency of quantum transport on them.
