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The problem of aligning Erd\"os-R\'enyi random graphs is a noisy,average-case version of the graph isomorphism problem, in which a pair ofcorrelated random graphs is observed through a random permutation of theirvertices. We study a polynomial time message-passing algorithm devised to solvethe inference problem of partially recovering the hidden permutation, in thesparse regime with constant average degrees. We perform extensive numericalsimulations to determine the range of parameters in which this algorithmachieves partial recovery. We also introduce a generalized ensemble ofcorrelated random graphs with prescribed degree distributions, and extend thealgorithm to this case.

Aligning random graphs with a sub-tree similarity message-passing algorithm