# Bootstrapping Networks with Latent Space Structure

arXiv: https://arxiv.org/abs/1907.10821 · HTML: https://mlsanity.com/paper/1907.10821/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2019.

## Built on by (most cited first, 12 of 12)

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- [Weighted Random Dot Product Graphs](https://mlsanity.com/paper/2505.03649/) (2025)
- [LOBSTUR: A Local Bootstrap Framework for Tuning Unsupervised Representations in Graph Neural Networks](https://mlsanity.com/paper/2505.14867/) (2025)
- [Block Dense Weighted Networks with Augmented Degree Correction](https://mlsanity.com/paper/2105.12290/) (2021)
- [Pitfalls of Climate Network Construction: A Statistical Perspective](https://mlsanity.com/paper/2211.02888/) (2022)
- [Bias-Corrected Joint Spectral Embedding for Multilayer Networks with Invariant Subspace: Entrywise Eigenvector Perturbation and Inference](https://mlsanity.com/paper/2406.07849/) (2024)
- [Valid Bootstraps for Network Embeddings with Applications to Network Visualisation](https://mlsanity.com/paper/2410.20895/) (2024)
- [Asymptotically perfect seeded graph matching without edge correlation (and applications to inference)](https://mlsanity.com/paper/2506.02825/) (2025)
- [Efficient Synthetic Network Generation via Latent Embedding Reconstruction](https://mlsanity.com/paper/2606.00934/) (2026)
- [Rethinking Epistemic Uncertainty in Node Classification through Information Growth](https://mlsanity.com/paper/2610.03418/) (2026)

## Abstract (arXiv)

A core problem in statistical network analysis is to develop network analogues of classical techniques. The problem of bootstrapping network data stands out as especially challenging, since typically one observes only a single network, rather than a sample. Here we propose two methods for obtaining bootstrap samples for networks drawn from latent space models. The first method generates bootstrap replicates of network statistics that can be represented as U-statistics in the latent positions, and avoids actually constructing new bootstrapped networks. The second method generates bootstrap replicates of whole networks, and thus can be used for bootstrapping any network function. Commonly studied network quantities that can be represented as U-statistics include many popular summaries, such as average degree and subgraph counts, but other equally popular summaries, such as the clustering coefficient, are not expressible as U-statistics and thus require the second bootstrap method. Under the assumption of a random dot product graph, a type of latent space network model, we show consistency of the proposed bootstrap methods. We give motivating examples throughout and demonstrate the effectiveness of our methods on synthetic data.