Matrimonial circuits in kinship networks: Calculation, enumeration and census

The article presents a series of new methods for analyzing the morphology of kinship networks via the study of matrimonial circuits (closed chains of kinship and marriage ties). The article gives a simple definition of matrimonial circuits in mixed graphs and introduces the technique of representing matrimonial circuit types by characteristic vectors. This technique is used to develop (1) an arithmetic approach to the algebra of circuit composition, (2) a method for the complete enumeration of matrimonial circuit types, and (3) an algorithm for finding and counting matrimonial circuits in empirical kinship networks. All methods have been implemented in the software Puck (Program for the Use and Computation of Kinship Data).