  Networks model a variety of complex phenomena across different domains. In
many applications, one of the most essential tasks is to align two or more
networks to infer the similarities between cross-network vertices and discover
potential node-level correspondence. In this paper, we propose ELRUNA
(Elimination rule-based network alignment), a novel network alignment algorithm
that relies exclusively on the underlying graph structure. Under the guidance
of the elimination rules that we defined, ELRUNA computes the similarity
between a pair of cross-network vertices iteratively by accumulating the
similarities between their selected neighbors. The resulting cross-network
similarity matrix is then used to infer a permutation matrix that encodes the
final alignment of cross-network vertices. In addition to the novel alignment
algorithm, we also improve the performance of local search, a commonly used
post-processing step for solving the network alignment problem, by introducing
a novel selection method RAWSEM (Randomwalk based selection method) based on
the propagation of the levels of mismatching (defined in the paper) of vertices
across the networks. The key idea is to pass on the initial levels of
mismatching of vertices throughout the entire network in a random-walk fashion.
Through extensive numerical experiments on real networks, we demonstrate that
ELRUNA significantly outperforms the state-of-the-art alignment methods in
terms of alignment accuracy under lower or comparable running time. Moreover,
ELRUNA is robust to network perturbations such that it can maintain a close to
optimal objective value under a high level of noise added to the original
networks. Finally, the proposed RAWSEM can further improve the alignment
quality with a less number of iterations compared with the naive local search
method.

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