The aim of this paper is develop a software module to test the connectivity of various odd-sized HRs and attempted to answer an open question whether the node connectivity of an odd-sized HR is equal to its degree. We attempted to answer this question by explicitly testing the node connectivity's of various oddsized HRs. In this paper, we also study the properties, constructions, and connectivity of hyper-rings. We usually use a graph to represent the architecture of an interconnection network,

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... where nodes represent processors and edges represent communication links between pairs of processors. Although the number of edges in a hyper-ring is roughly twice that of a hypercube with the same number of nodes, the diameter and the connectivity of the hyper-ring are shorter and larger, respectively, than those of the corresponding hypercube. These properties are advantageous to hyper-ring as desirable interconnection networks. This paper discusses the reliability in hyper-ring. One of the major goals in network design is to find the best way to increase the system's reliability. The reliability of a distributed system depends on the reliabilities of its communication links and computer elements.