Identifying Polycentric Urban Structure Using the Minimum Cycle Basis of Road Network as Building Blocks.

A graph's minimum cycle basis is defined as the smallest collection of cycles that exhibit linear independence in the cycle space, serving as fundamental building blocks for constructing any cyclic structure within the graph. These bases are useful in various contexts, including the intricate analysis of electrical networks, structural engineering endeavors, chemical processes, and surface reconstruction techniques, etc. This study investigates the urban road networks of six Chinese cities to analyze their topological features, node centrality, and robustness (resilience to traffic disruptions) using motif analysis and minimum cycle bases methodologies. Some interesting conclusions are obtained: the frequency of motifs containing cycles exceeds that of random networks with equivalent degree sequences; the frequency distribution of minimum cycle lengths and surface areas obeys the power-law distribution. The cycle contribution rate is introduced to investigate the centrality of nodes within road networks, and has a significant impact on the total number of cycles in the robustness analysis. Finally, we construct two types of cycle-based dual networks for urban road networks by representing cycles as nodes and establishing edges between two cycles sharing a common node and edge, respectively. The results show that cycle-based dual networks exhibit small-world and scale-free properties. The research facilitates a comprehensive understanding of the cycle structure characteristics in urban road networks, thereby providing a theoretical foundation for both subsequent modeling endeavors of transportation networks and optimization strategies for existing road infrastructure.