On the reciprocity of connections in weighted and unweighted networks

Bivariate Bernoulli and bivariate geometric distributions are proposed to model reciprocity in weighted and unweighted networks. Sampling properties of commonly used reciprocity measures are studied, under both presence and absence of reciprocity. Extensions to situations where link parameters depend on outgoing and incoming nodes are investigated. Results are illustrated with a data set, on 50 anesthesia providers at a hospital, that describes the number of times an anesthesia provider starting an operation transfers his/her responsibilities to another anesthesia provider.