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Abstract:
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The literature on network science abounds with diverse community detection methods. Included among them, modularity optimization has found widespread application and success. From a statistical physics perspective, modularity optimization and its variants are equivalent to ground state determination of the Potts model. We extend this notion to include the external field in the Potts energy function to impose constraints on the derived communities. The incorporation of external information of a global nature has remained largely unstudied. We retain the probabilistic aspect of the Potts model with an external field to define an MCMC sampling regime for the community labels. We apply this novel method to a network of hospitals, some of which are specialized. Our constraint is that each health care community (HCC) must contain at least one specialized hospital. For one to make meaningful comparisons among discovered communities, a level of homogeneity of resource availability is necessary. The specialized hospitals are equipped to implant implantable cardiac defibrillators (ICDs) and, while all hospitals are partitioned into HCCs, we require that each HCC contain at least one ICD capable hospital.
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