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

Abstract

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.

References in corpus (12)

• Finding and evaluating community structure in networks
• Graph limits and exchangeable random graphs
• Network histograms and universality of blockmodel approximation
• On a 'Two Truths' Phenomenon in Spectral Graph Clustering
• Entrywise Eigenvector Analysis of Random Matrices with Low Expected Rank
• A central limit theorem for an omnibus embedding of multiple random graphs and implications for multiscale network inference
• Two-Sample Tests for Large Random Graphs Using Network Statistics
• Bootstrapping Networks with Latent Space Structure
• Unified ${\ell }_{2\to \infty }$ Eigenspace Perturbation Theory for Symmetric Random Matrices
• Two-sample Test of Community Memberships of Weighted Stochastic Block Models
• Network Representation Using Graph Root Distributions
• Uniform bounds for invariant subspace perturbations

Cited by in corpus (2)

• Nonparametric two-sample hypothesis testing for low-rank random graphs of differing sizes
• Valid Two-Sample Graph Testing via Optimal Transport Procrustes and Multiscale Graph Correlation with Applications in Connectomics