LAUSR

Using complex network analysis methods to analyze the internal structure of geographic networks is a popular topic in urban geography research. Statistical analysis occupies a dominant position in the current research on geographic networks. This perspective mainly focuses on node connectivity, while other perspectives, such as geometric and algebraic perspectives, can provide additional insights into network structure. Using 11 different real-world geographic networks as examples, this study examines geographic networks from statistical, geometric, and algebraic perspectives. The following are some of the paper’s new findings: (1) When viewed statistically, geometrically, and algebraically, geographic networks have completely different properties. The statistical perspective describes both local and global connectivity; the Ricci curvature in the geometric perspective can assess the network’s development potential as well as describe its transmission capability, and the algebraic perspective can capture the global network topology other than connectivity; (2) Networks are qualitatively and quantitatively classified from three perspectives. The classification results are in accordance with the topological robustness experiment results, which indicate that an analysis from many angles has a lot of practical relevance; (3) Statistical indicators are better than Ricci curvature in identifying essential nodes in networks from a geometric standpoint, whereas the latter is better at detecting significant edges. Overall, studying geographic networks from various perspectives may provide new insights into their understanding.