# Modeling Random Networks with Heterogeneous Reciprocity

arXiv: https://arxiv.org/abs/2308.10113 · HTML: https://mlsanity.com/paper/2308.10113/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 19 Aug 2023.

## Builds on (most cited first, 14 of 14)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)
- [Statistical clustering of temporal networks through a dynamic stochastic block model](https://mlsanity.com/paper/1506.07464/) (2015)
- [Mixture models with a prior on the number of components](https://mlsanity.com/paper/1502.06241/) (2015)
- [Model-based clustering based on sparse finite Gaussian mixtures](https://mlsanity.com/paper/1606.06828/) (2016)
- [Finite mixture models do not reliably learn the number of components](https://mlsanity.com/paper/2007.04470/) (2020)
- [Science, AskScience, and BadScience: On the Coexistence of Highly Related Communities](https://mlsanity.com/paper/1612.07487/) (2016)
- [Probabilistic community detection with unknown number of communities](https://mlsanity.com/paper/1602.08062/) (2016)
- [Generalized mixtures of finite mixtures and telescoping sampling](https://mlsanity.com/paper/2005.09918/) (2020)
- [A Directed Preferential Attachment Model with Poisson Measurement](https://mlsanity.com/paper/2008.07005/) (2020)
- [Reciprocity in Social Networks with Capacity Constraints](https://mlsanity.com/paper/1412.4299/) (2014)
- [Fitting the Linear Preferential Attachment Model](https://mlsanity.com/paper/1703.03095/) (2017)
- [Likelihood-based Inference for Random Networks with Changepoints](https://mlsanity.com/paper/2206.01076/) (2022)
- [Random Networks with Heterogeneous Reciprocity](https://mlsanity.com/paper/2208.00348/) (2022)

## Abstract (arXiv)

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.