Collective flow-evolutionary patterns reveal the mesoscopic structure between snapshots of spatial network

Uncovering the collective behavior of flows among locations is critical to understanding the structure within an ever-changing spatial network. When a network evolves, there may exist subgraphs within which the internal flows generally follow a rule: the change rates of the flow weight are either collectively high or low. Classic network measures such as degree, clustering, and betweenness can be used to quantify the process of network evolution by profiling the overall characteristics over time. However, it remains challenging to elucidate how a spatial network is evolving without looking at structures where collective changes emerge. To bridge this gap, we introduce the concept of the Collective Flow-Evolutionary Pattern (CFEP) as a mesoscopic description for spatial network evolution. Four types of patterns with distinct features are defined to clarify the collective behaviors of the flow-evolutionary characteristics. We provide an analytical framework that utilizes flow change rates between two snapshots of the spatial network to detect CFEPs as optimized flow evolution (evo-groups). Synthetic experiments are presented to validate the method. A case study of large-scale individual mobile positioning data is conducted in the Twin Cities Metropolitan Area, Minnesota, US to demonstrate how CFEP can effectively understand the evolution of human mobility networks.