  Urban spaces, though often perceived as discrete communities, are shared by
various functional and social groups. Our study introduces a graph-based
physics-aware deep learning framework, illuminating the intricate overlapping
nature inherent in urban communities. Through analysis of individual mobile
phone positioning data at Twin Cities metro area (TCMA) in Minnesota, USA, our
findings reveal that 95.7 % of urban functional complexity stems from the
overlapping structure of communities during weekdays. Significantly, our
research not only quantifies these overlaps but also reveals their compelling
correlations with income and racial indicators, unraveling the complex
segregation patterns in U.S. cities. As the first to elucidate the overlapping
nature of urban communities, this work offers a unique geospatial perspective
on looking at urban structures, highlighting the nuanced interplay of
socioeconomic dynamics within cities.
