# On Two Distinct Sources of Nonidentifiability in Latent Position Random Graph Models

arXiv: https://arxiv.org/abs/2003.14250 · HTML: https://mlsanity.com/paper/2003.14250/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2020.

## Built on by (most cited first, 6 of 6)

- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
- [Spectral embedding and the latent geometry of multipartite networks](https://mlsanity.com/paper/2202.03945/) (2022)
- [Perfect Spectral Clustering with Discrete Covariates](https://mlsanity.com/paper/2205.08047/) (2022)
- [Adversarial contamination of networks in the setting of vertex nomination: a new trimming method](https://mlsanity.com/paper/2208.09710/) (2022)
- [Signal Recovery from Random Dot-Product Graphs Under Local Differential Privacy](https://mlsanity.com/paper/2504.17274/) (2025)
- [Asymptotically perfect seeded graph matching without edge correlation (and applications to inference)](https://mlsanity.com/paper/2506.02825/) (2025)

## Abstract (arXiv)

Two separate and distinct sources of nonidentifiability arise naturally in the context of latent position random graph models, though neither are unique to this setting. In this paper we define and examine these two nonidentifiabilities, dubbed subspace nonidentifiability and model-based nonidentifiability, in the context of random graph inference. We give examples where each type of nonidentifiability comes into play, and we show how in certain settings one need worry about one or the other type of nonidentifiability. Then, we characterize the limit for model-based nonidentifiability both with and without subspace nonidentifiability. We further obtain additional limiting results for covariances and U-statistics of stochastic block models and generalized random dot product graphs.