In this paper we study isomorphism between circulant graphs. Such graphs have a vast number of applications to telecommunication network, VLSI design and distributed computation [4,13,15,17]. By suitably choosing the length of the chord between two nodes of the network, one can achieve the appropriate property: e.g., low diameter, high connectivity, or implicit routing. A network that does provide labelled edges should be able to exploit the same properties as one with different labelling if the underlying graphs are isomorphic.