# A Directed Preferential Attachment Model with Poisson Measurement

arXiv: https://arxiv.org/abs/2008.07005 · HTML: https://mlsanity.com/paper/2008.07005/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Aug 2020.

## Built on by (most cited first, 2 of 2)

- [Modeling Random Networks with Heterogeneous Reciprocity](https://mlsanity.com/paper/2308.10113/) (2023)
- [Causal Models for Growing Networks](https://mlsanity.com/paper/2504.01012/) (2025)

## Abstract (arXiv)

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.