The purpose of this study is to develop a theoretical formula for the average forwarding distance and construct a usable cyclic path model to clarify the relationship between a road network and its average forwarding distance. Initially, the probability distribution function of the forwarding distance and the graph theory to formulate the average forwarding distance is introduced. On this basis, the average forwarding distance could be calculated from the forwarding distance, degree and in-degree of each vertex, including the road fork and end point-node. In particular, the average forwarding distance of the road network without cyclic pahts could be calculated using only the forwarding distance and degree of each vertex. Next, we presented a ladder-type model as a cyclic path model to evaluate the relationship between the average forwarding distance calculated with this model and the actual one. The results obtained suggest that this model was applicable to an actual high-density road network, due to the positive correlation between the average forwarding distances. This model was thus evaluated as an effective means of analyzing the relationship between a road network and its average forwarding distance.

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