  We analyse the eigenvectors of the adjacency matrix of the Erd\H{o}s-R\'enyi
graph on $N$ vertices with edge probability $\frac{d}{N}$. We determine the
full region of delocalization by determining the critical values of
$\frac{d}{\log N}$ down to which delocalization persists: for $\frac{d}{\log N}
> \frac{1}{\log 4 - 1}$ all eigenvectors are completely delocalized, and for
$\frac{d}{\log N} > 1$ all eigenvectors with eigenvalues away from the spectral
edges are completely delocalized. Below these critical values, it is known
[arXiv:2005.14180, arXiv:2106.12519] that localized eigenvectors exist in the
corresponding spectral regions.
