In this paper we present two algorithms for computing the extent of regular equivalence among pairs of nodes in a network. The first algorithm, REGE, is well known, but has not previously been described in the literature. The second algorithm, CATREGE, is new. Whereas REGE is applicable to quantitative data, CATREGE is used for categorical data. For binary data, either algorithm may be used, though the CATREGE algorithm is significantly faster and its output similarity coefficients have better metric properties. The CATREGE algorithm is also useful pedagogically, because it is easier to grasp.