Reciprocity in marital and social networks: illustration with Indian data

Three measures of reciprocity, denoted s2, s3, and s4, that are applicable to both simple and weighted networks are considered here. By reciprocity I mean symmetry or mutuality of ties between different vertices of the network. These measures have simple formulas except in some extreme situations and can be used for most networks. Among the three measures, s2 is generally preferred, although the choice in any situation depends on the validity of the assumptions underlying its derivation and its discriminating power. I illustrate how reciprocity in the network of marital exchanges between different surnames and settlements can reveal something about the structure of a population. Reciprocity is higher if the endogamous group is close-knit, is well settled in a smaller geographic area, and has a low surname diversity index. Thus reciprocity is high in the Vadde, somewhat high in the Pattusali, and low in the Yanadi. Although s2, s3, and s4 measure reciprocity in a network as a whole, the local reciprocity index can be used to see how reciprocally a particular vertex is tied to others and can help in the study of the direction of the exchanges. The low local reciprocity indexes of the neighborhood settlements of the Yanadi in some regions indicate that the settlements are involved in one-way marital exchanges with other settlements. The study of reciprocity can be relevant in other contexts also. High reciprocity in a well-settled population was also observed in the social networks of 21 villages with respect to the "help" relation. It was found that reciprocity is highly negatively correlated with the percentage of migrants in the village but does not show high positive or negative correlation with other demographic, socioeconomic, and location characteristics of the villages.