A Latent Space Approach to Inferring Distance-Dependent Reciprocity in Directed Networks

TL;DR

This paper presents a novel latent space model for directed networks that captures heterogeneous reciprocity patterns based on actors' latent distances, enabling better understanding of mutual relationship tendencies.

Contribution

It introduces a flexible latent space model that accounts for heterogeneity in reciprocity, extending existing models and allowing for meaningful comparisons.

Findings

Identified diverse reciprocity patterns in real-world networks.

Demonstrated the model's ability to distinguish different reciprocity behaviors.

Provided a Bayesian inference method using Hamiltonian Monte Carlo.

Abstract

Reciprocity, or the stochastic tendency for actors to form mutual relationships, is an essential characteristic of directed network data. Existing latent space approaches to modeling directed networks are severely limited by the assumption that reciprocity is homogeneous across the network. In this work, we introduce a new latent space model for directed networks that can model heterogeneous reciprocity patterns that arise from the actors' latent distances. Furthermore, existing edge-independent latent space models are nested within the proposed model class, which allows for meaningful model comparisons. We introduce a Bayesian inference procedure to infer the model parameters using Hamiltonian Monte Carlo. Lastly, we use the proposed method to infer different reciprocity patterns in an advice network among lawyers, an information-sharing network between employees at a manufacturing company, and a friendship network between high school students.