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 to discover potential node-level correspondence. In this article, we propose ELRUNA (
el
imination
ru
le-based
n
etwork
a
lignment), 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 improve the performance of
local search
, a commonly used postprocessing step for solving the network alignment problem, by introducing a novel selection method RAWSEM (
ra
ndom-
w
alk-based
se
lection
m
ethod) based on the propagation of vertices’ mismatching 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 smaller number of iterations compared with the naive local search method.
Reproducibility
: The source code and data are available at https://tinyurl.com/uwn35an.
Local search for the generalized tree alignment problem
