The most important characteristic of Massively Parallel Computing systems is the topology of the network that means how to connect the processors with each other so that provides fast data transfer and low cost. In this research, we will find new link networks that provide speed in the transport and low cost compared with other traditional networks for connecting processors. Interconnection networks are divided to be static networks so that fixed links between processors, while dynamic networks so that every communication between two processors owns more than one path. Each network differs from the other in cost which express the number of links within this network, and speed which express the network diameter and bisection. The network is best whenever the cost is less and diameter is less but bisection is larger. In this research I compared between these networks and then look for new networks through hybridization between core networks. After that I studied the specification of hybrid interconnections compared with its constituent core networks.