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

Efficiently matching random inhomogeneous graphs via degree profiles