Identifying polycentric urban structure using the minimum cycle basis of road network as building blocks

In a graph, the minimum cycle bases are a set of linearly independent cycles that can be used to represent any cycle within that cycle space of 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 focuses on six cities in China to explore the topological characteristics, the centrality of nodes and robustness of urban road networks based on motif and minimum cycle bases. 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's length and surface areas obey 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.