  Reciprocity characterizes the information exchange between users in a
network, and some empirical studies have revealed that social networks have a
high proportion of reciprocal edges. Classical directed preferential attachment
(PA) models, though generating scale-free networks, may give networks with low
reciprocity. This points out one potential problem of fitting a classical PA
model to a given network dataset with high reciprocity, and indicates
alternative models need to be considered. We give one possible modification of
the classical PA model by including another parameter which controls the
probability of adding a reciprocated edge at each step. Asymptotic analyses
suggest that large in- and out-degrees become fully dependent in this modified
model, as a result of the additional reciprocated edges.
