High performance computing (HPC) means the aggregation of computational power to increase the ability of processing large problems in science, engineering, and business. HPC on the cloud allows performing on demand HPC tasks by high performance clusters in a cloud environment. The connection structure of the nodes in HPC clusters should provide fast internode communication. It is important that scalability is preserved as well. This paper proposes a hypercube topology for connecting the nodes in an HPC cluster that facilitates fast communications between nodes. In addition, the proposed hypercube topology provides the ability to scale, which is needed for high performance computing on the cloud.