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Based on Clifford algebra, a shortest path analysis algorithm is proposed in this paper. Dimensions free distance and intersection operators are defined in a homogeneous space. By using these operators, we extract the adjacency matrix automatically from geographical network data. Locally dynamical layer separation and shortest path query mechanism are constructed based on the outer product. The experiment on China National Highway Road data suggests that the algorithm is comparable in both result and computational performance, and with the potentiality to extend to higher dimensions.