An approach for exploring spatial associations in multi-layer networks based on convergent and divergent flow structures

The study of spatial social networks has evolved from identifying structures within single networks to analyzing spatial associations between multilayer networks. However, current research primarily focuses on many-to-many flow structures, neglecting the unique advantages of one-to-many flow in characterizing local and global interactions. To bridge this gap, this paper introduces flow sequences and flow structure curves to effectively represent and visualize structures of one-to-many flows. Building on this foundation, a similarity-based comparison strategy to analyze spatial associations of one-to-many flow structures within two different networks from a local perspective is proposed. This method can be utilized to examine associations across diverse scenarios, including between distinct networks, within a single network over different temporal intervals, and between the inflow and outflow of the same network. The effectiveness and robustness of the proposed method were validated using a synthetic dataset. Case studies on migration and attention flows demonstrated its diverse applications and potential. The proposed approach enhances convergent and divergent analysis in multi-semantic spatial networks by offering tools for investigating structural consistency across networks. It emphasizes the influence of individual nodes on the entire network and the reciprocal shaping of local interaction relationships by global patterns.