  Graph alignment in two correlated random graphs refers to the task of
identifying the correspondence between vertex sets of the graphs. Recent
results have characterized the exact information-theoretic threshold for graph
alignment in correlated Erd\H{o}s-R\'enyi graphs. However, very little is known
about the existence of efficient algorithms to achieve graph alignment without
seeds.
  In this work we identify a region in which a straightforward $O(n^{11/5} \log
n )$-time canonical labeling algorithm, initially introduced in the context of
graph isomorphism, succeeds in aligning correlated Erd\H{o}s-R\'enyi graphs.
The algorithm has two steps. In the first step, all vertices are labeled by
their degrees and a trivial minimum distance alignment (i.e., sorting vertices
according to their degrees) matches a fixed number of highest degree vertices
in the two graphs. Having identified this subset of vertices, the remaining
vertices are matched using a alignment algorithm for bipartite graphs.
