  We study the coherent exciton transport of continuous-time quantum walks
(CTQWs) on Erdos-Renyi networks. The Erdos-Renyi network of N nodes is
constructed by connecting every pair of nodes with probability $p$. We
numerically calculate the ensemble averaged transition probability of quantum
transport between two nodes of the networks. For finite networks, we find that
the limiting transition probability is reached very quickly. For infinite
networks whose spectral density follows the semicircle law, the efficiencies of
the classical and quantum-mechanical transport are compared on networks of
different average degree. In the long time limiting, we consider the
distribution of the ensemble averaged transition probabilities, and show that
there is a high probability to find the exciton at the initial node. Such high
return probability almost do not alter in a wide range of connection
probability p but increases rapidly when the network approaches to be fully
connected. For networks whose topology is not extremely connected, the return
probability is inversely proportional to the network size N. Furthermore, the
transport dynamics are compared with that on a random graph model in which the
degree of each node equals to the average degree of the Erdos-Renyi networks.
