Title: Potential landscape of human flow in cities

Abstract:
[Addressed problem: How to visualize human flow on map?] People are moving from one location to another in their daily lives, for commuting, shopping, entertainment, schools, etc. This human flow provides vital information for unfolding the actual shapes of cities based on lively human behavior by place-to-place interactions from origin to destination. However, it is not easy to handle massive data on human flows as it is because, for example, when there are 1,000 locations on a map, the flow dataset is depicted by a million links from the origin to the destination.

[Our solution: Use combinatorial Hodge theory to obtain the potential of the human flow] In this study, we identified the potential of human flow directly from a given origin-destination matrix. By using a metaphor for water flowing from a higher place to a lower place, the potential landscape visualizes an intuitive perspective of the human flow and determines the map of urban structure behind the massive movements of people. From the map, we can easily identify the sinks (attractive places) and the sources of human flow, not just populated places. The detected attractive places provide beneficial information for location decision making for commercial or public buildings, optimization of transportation systems, urban planning by policy makers, and measures for movement restrictions under a pandemic.