Asymptotic dependence of in- and out-degrees in a preferential attachment model with reciprocity

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