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Detecting American regions using migration data and community detection in graphs

What is the Midwest? Where is the South? Where's the gateway to the West? How do we define the regions of the United States? Plenty of folks have answered this question, and many have taken a quantitative approach. Take a look:

Earth features

Economic and cultural features

Social interactions

Aggregations and crowdsourcing

And of course, Wikipedia's List of regions of the United States and Regions of the United States category.

My approach

  1. Migration data
  2. Graph data structures
  3. Graph community detection methods
  4. Probablistic method that gives us "fuzzy" community detection
  5. Regions are defined by a county of interest. That is, for any given County C, what proportion of the time does any other County X fall into the same detected community?