# Time-varying β-model for dynamic directed networks

arXiv: https://arxiv.org/abs/2304.02421 · HTML: https://mlsanity.com/paper/2304.02421/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [Privacy utility trade offs for parameter estimation in degree heterogeneous higher order networks](https://mlsanity.com/paper/2602.03948/) (2026)

## Abstract (arXiv)

We extend the well-known β-model for directed graphs to dynamic network setting, where we observe snapshots of adjacency matrices at different time points. We propose a kernel-smoothed likelihood approach for estimating 2n time-varying parameters in a network with n nodes, from N snapshots. We establish consistency and asymptotic normality properties of our kernel-smoothed estimators as either n or N diverges. Our results contrast their counterparts in single-network analyses, where n→∞ is invariantly required in asymptotic studies. We conduct comprehensive simulation studies that confirm our theory's prediction and illustrate the performance of our method from various angles. We apply our method to an email data set and obtain meaningful results.