  In this paper, we study the problem of recovering the latent vertex
correspondence between two correlated random graphs with vastly inhomogeneous
and unknown edge probabilities between different pairs of vertices. Inspired by
and extending the matching algorithm via degree profiles by Ding, Ma, Wu and Xu
(2021), we obtain an efficient matching algorithm as long as the minimal
average degree is at least $\Omega(\log^{2} n)$ and the minimal correlation is
at least $1 - O(\log^{-2} n)$.
