Finding topological center of a geographic space via road network

• Road-Cycle Detection (RCD) method is designed and implemented.
• RCD finds the same topological center with the previous Block Detection (BD).
• RCD is at least seven times more efficient than BD on ten typical road networks.
• An ArcGIS implementation of RCD is provided for those who are familiar with GIS.

Previous studies show that the center of a geographic space is of great importance in urban and regional studies, including study of population distribution, urban growth modeling, and scaling properties of urban systems, etc. But how to well define and how to efficiently extract the center of a geographic space are still largely unknown. Recently, Jiang et al. have presented a definition of topological center by their block detection (BD) algorithm. Despite the fact that they first introduced the definition and discovered the ‘true center’, in human minds, their algorithm left several redundancies in its traversal process. Here, we propose an alternative road-cycle detection (RCD) algorithm to find the topological center, which extracts the outmost road-cycle recursively. To foster the application of the topological center in related research fields, we first reproduce the BD algorithm in Python (pyBD), then implement the RCD algorithm in two ways: the ArcPy implementation (arcRCD) and the Python implementation (pyRCD). After the experiments on twenty-four typical road networks, we find that the results of our RCD algorithm are consistent with those of Jiang’s BD algorithm. We also find that the RCD algorithm is at least seven times more efficient than the BD algorithm on all the ten typical road networks.