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Social network analysis is a methodology used extensively in social science. Classical social networks can only represent the qualitative relationships between actors, but weighted social networks can describe the degrees of connection between actors. In a classical social network, regular equivalence is used to capture the similarity between actors based on their links to other actors. Specifically, two actors are deemed regularly equivalent if they are equally related to equivalent others. The definition of regular equivalence has been extended to weighted social networks in two ways. The first definition, called regular similarity, considers regular equivalence as an equivalence relation that commutes with the underlying graph edges; while the second definition, called generalized regular equivalence, is based on the notion of role assignment or coloring. A role assignment (resp. coloring) is a mapping from the set of …