Quantifying social asymmetric structures

Many social phenomena involve a set of dyadic relations among agents whose actions may be dependent. Although individualistic approaches have frequently been applied to analyze social processes, these are not generally concerned with dyadic relations, nor do they deal with dependency. This article describes a mathematical procedure for analyzing dyadic interactions in a social system. The proposed method consists mainly of decomposing asymmetric data into their symmetric and skew-symmetric parts. A quantification of skew symmetry for a social system can be obtained by dividing the norm of the skew-symmetric matrix by the norm of the asymmetric matrix. This calculation makes available to researchers a quantity related to the amount of dyadic reciprocity. With regard to agents, the procedure enables researchers to identify those whose behavior is asymmetric with respect to all agents. It is also possible to derive symmetric measurements among agents and to use multivariate statistical techniques.