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We explored the use of Self Organizing Map (SOM) to assess the problem of efficiency measurement in the case of health care providers. To do this, we used as input the data from the balance sheets of 300 health care providers, as resulting from the Italian Statistics Institute (ISTAT) database, and we examined their representation obtained both by running classical SOM algorithm, and by modifying it through the replacement of standard Euclidean distance with the generalized Minkowski metrics. Finally, we have shown how the results may be employed to perform graph mining on data. In this way, we were able to discover intrinsic relationships among health care providers that, in our opinion, can be of help to stakeholders to improve the quality of health care service. Our results seem to contribute to the existing literature in at least two ways: (a) using SOM to analyze data of health care providers is completely new; (b) SOM graph mining shows, in turn, elements of innovations for the way the adjacency matrix is formed, with the connections among SOM winner nodes used as starting point to the process.