A Directed Preferential Attachment Model with Poisson Measurement

TL;DR

This paper introduces a modified directed preferential attachment model incorporating Poisson measurement to better reflect real social network growth with coarse timestamps, showing improved fit over traditional models.

Contribution

It proposes a new preferential attachment model with Poisson measurement that accounts for coarse timestamp data and demonstrates its superior fit to real social network datasets.

Findings

The model captures non-homogeneous Poisson process behavior in network growth.

It fits real datasets better than traditional preferential attachment models.

The asymptotic analysis provides insights into the model's long-term behavior.

Abstract

When modeling a directed social network, one choice is to use the traditional preferential attachment model, which generates power-law tail distributions. In a traditional directed preferential attachment, every new edge is added sequentially into the network. However, for real datasets, it is common to only have coarse timestamps available, which means several new edges are created at the same timestamp. Previous analyses on the evolution of social networks reveal that after reaching a stable phase, the growth of edge counts in a network follows a non-homogeneous Poisson process with a constant rate across the day but varying rates from day to day. Taking such empirical observations into account, we propose a modified preferential attachment model with Poisson measurement, and study its asymptotic behavior. This modified model is then fitted to real datasets, and we see it provides a better fit than the traditional one.