Modeling Random Networks with Heterogeneous Reciprocity

TL;DR

This paper introduces a novel preferential attachment model with heterogeneous reciprocity to better understand diverse reciprocal behaviors in social networks, capturing community structures and degree distributions.

Contribution

It develops a new modeling framework for heterogeneous reciprocity in growing social networks and compares Bayesian and frequentist fitting methods, including variational approaches.

Findings

Model captures heavy-tailed degree distributions.

Identifies multiple user groups with different reciprocity patterns.

Effectively fits Facebook wallpost network data.

Abstract

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.