The authors present a comparative study of three different interconnection networks for possible application as the logical interconnection in a lightwave network. They outline a new network topology called supercube and study its performance with respect to the shuffle exchange network and the Manhattan street network. The static characteristics of the networks have been studied through their graph theoretic properties. The dynamic characteristics of the network have been studied through simulation. The results of the simulation study shows that the supercube network outperforms the other two networks consistently.