  For two correlated graphs which are independently sub-sampled from a common
Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their
\emph{latent} vertex matching from the observation of these two graphs
\emph{without labels}. When $p = n^{-\alpha+o(1)}$ for $\alpha\in (0, 1]$, we
establish a sharp information-theoretic threshold for whether it is possible to
correctly match a positive fraction of vertices. Our result sharpens a constant
factor in a recent work by Wu, Xu and Yu.
