Topological Properties of Hypercubes

The n-dimensional hypercube is a highly concurrent loosely coupled multiprocessor based on the binary n-cube topology. Machines based on the hypercube topology have been advocated as ideal parallel architectures for their powerful interconnection features. In this paper, we examine the hypercube from the graph theory point of view and consider those features that make its connectivity so appealing. Among other things, we propose a theoretical characterization of the n-cube as a graph and show how to map various other topologies into a hypercube.