  Human flow data are rich behavioral data relevant to people's decision-making
regarding where to live, work, go shopping, etc., and provide vital information
for identifying city centers. However, it is not as easy to understand massive
relational data, and datasets have often been reduced merely to the statistics
of trip counts at destinations, discarding relational information from origin
to destination. In this study, we propose an alternative center identification
method based on human mobility data. This method extracts the scalar potential
field of human trips based on combinatorial Hodge theory. It detects not only
statistically significant attractive locations as the sinks of human trips but
also significant origins as the sources of trips. As a case study, we identify
the sinks and sources of commuting and shopping trips in the Tokyo metropolitan
area. This aim-specific analysis leads to a combinatorial classification of
city centers based on the distinct aspects of human mobility. The proposed
method can be applied to other mobility datasets with relevant properties and
helps us examine the complex spatial structures in contemporary metropolitan
areas from the multiple perspectives of human mobility.
