Preferential Attachment with Reciprocity: Properties and Estimation

TL;DR

This paper extends the classical directed preferential attachment model by incorporating reciprocity and edge creation between existing nodes, providing a better fit to real social network data and analyzing its theoretical properties and estimation methods.

Contribution

Introduces a new PA model with reciprocity and existing node edge creation, along with analysis and estimation procedures for real-world network fitting.

Findings

Model matches empirical degree distributions well

Estimation procedures are effective on simulated and real data

Further model generalization may improve fit

Abstract

Reciprocity in social networks helps understand information exchange between two individuals, and indicates interaction patterns between pairs of users. A recent study indicates the reciprocity coefficient of a classical directed preferential attachment (PA) model does not match empirical evidence. In this paper, we extend the classical 3-scenario directed PA model by adding an additional parameter that controls the probability of creating a reciprocal edge. Our proposed model also allows edge creation between two existing nodes, making it a more realistic choice for fitting to real datasets. In addition to analysis of the theoretical properties of this PA model with reciprocity, we provide and compare two estimation procedures for the fitting of the extended model to both simulated and real datasets. The fitted models provide a good match with the empirical tail distributions of both in- and out-degrees. Other mismatched diagnostics suggest that further generalization of the model is warranted.