Morris, Walter D JrBrown, Barbara A2018-08-082018-08-08https://hdl.handle.net/1920/11091Each cycle of a directed graph can be written as a linear combination of the circuits of a cycle basis for that directed graph. We define two new classes of cycle bases and show how each relates to the known classes of strictly fundamental cycle bases, zero-one cycle bases and integral cycle bases. We provide examples showing the significance of the Möbius band to constructing directed graphs, the bases of which are in some of these classes and not in other classes.enZero-one cycle basisCircuit boxed cycle basisIntegral cycle basisSimple cycle boxed cycle basisStrictly fundamental cycle basisCycle matrixThesis