Graph theory is a powerful mathematical tool that can be used in the study of computer network routing. In this paper, graph theory is adopted to find the Continuum of Unidirectional Edges (CUE) that walk through all the vertexes once and return to the starting vertex. For the resulted simple Fixed Hop Over (FHO) uniform routing algorithm, the sufficient condition is given to address questions like "Does a CUE exist? ", "How many of them exist?", and "How to find a CUE?". The sufficient condition is summarized in a theorem and proved mathematically. The results of the study can be used for the development of routing strategies applicable in many situations, including wireless sensor networks, where simple and uniform routing strategies are demanded. An example in this area is given at the end of the paper.
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