An optimizational approach to regular equivalence

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Abstract Most partitions of social network (relational) data are presented and interpreted with little attention to assessing the adequacy of the partitions. We present a new criterion function that operationalizes the concept of regular equivalence and provides a measure of the departure of any structure from an exact regular partition. We then use a local optimization procedure to locate partitions where the algorithm minimizes the criterion function. After applying these methods for constructed and empirical data sets, we compare our results with those obtained from using other methods.