Modeling Random Networks with Heterogeneous Reciprocity
Daniel Cirkovic Tiandong Wang
Reciprocity, or the tendency of individuals to mirror behavior, is a key
measure that describes information exchange in a social network. Users in
social networks tend to engage in different levels of reciprocal behavior.
Differences in such behavior may indicate the existence of communities that
reciprocate links at varying rates. In this paper, we develop methodology to
model the diverse reciprocal behavior in growing social networks. In
particular, we present a preferential attachment model with heterogeneous
reciprocity that imitates the attraction users have for popular users, plus the
heterogeneous nature by which they reciprocate links. We compare Bayesian and
frequentist model fitting techniques for large networks, as well as
computationally efficient variational alternatives. Cases where the number of
communities are known and unknown are both considered. We apply the presented
methods to the analysis of a Facebook wallpost network where users have
non-uniform reciprocal behavior patterns. The fitted model captures the
heavy-tailed nature of the empirical degree distributions in the Facebook data
and identifies multiple groups of users that differ in their tendency to reply
to and receive responses to wallposts.