Topological Properties of Hypercubes
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This paper proposes a novel architecture called KCube. KCube is a compound graph of Kautz digraph and hypercube. It employs the hypercube topology as a unit cluster and connects many such clusters by means of a Kautz digraph. It then utilizes the topological properties of hypercube to realize convenient embedding of parallel algorithms, and the short diameter of Kautz graph to support efficient inter-cluster communication. KCube possesses many attractive characteristics, such as modularity, expansibility, and regularity, while these benefits are achieved at the cost of only increasing the degree of any node by one, regardless of the network size. The methodology to construct KCube can also be applied to other compound networks after minimal modifications.