The present invention provides a mixed torus and hypercube multi-rank tensor expansion method which can be applied to the communication subsystem of a parallel processing system. The said expansion method is based on the conventional torus and hypercube topologies. A mixed torus and hypercube multi-rank tensor expansion interconnection network is built up by means of supernodes equipped with expansion interfaces. This method not only provides more bisection bandwidth to the entire system but also improves the long-range communication and global operations. Affirmatively, this expansion method can achieve better scalability and flexibility for the parallel system for a given system size.