Local bootstrap for network data.

The article focuses on a new bootstrap method for network analysis called the local bootstrap, designed to estimate standard errors of network statistics from a single observed network. Unlike existing methods that resample vertices directly and often perform poorly for small or moderate sample sizes due to complex vertex dependencies, the local bootstrap resamples vertices along with their neighbour sets and reconstructs edges by sampling from connections between these neighbour sets. The method is theoretically justified for statistics such as motif density, encompasses existing approaches like the empirical graphon bootstrap as special cases, and demonstrates superior finite-sample performance by better preserving vertex correlation and edge randomness. Numerical studies on simulated and real networks show that the local bootstrap provides more accurate standard error estimates and computational efficiency compared to several alternative methods, with flexibility to handle both binary and weighted networks.