Graph matching beyond perfectly-overlapping Erdős–Rényi random graphs

Abstract Graph matching is a fruitful area in terms of both algorithms and theories. Given two graphs $$G_1 = (V_1, E_1)$$ G 1 = ( V , E ) $$G_2 (V_2, E_2)$$ 2 , where $$V_1$$ $$V_2$$ are the same or largely overlapped upon an unknown permutation $$\pi ^*$$ π ∗ graph to seek correct mapping . In this paper, we exploit degree information, which was previously used only noiseless perfectly-overlapping Erdős–Rényi random matching. We concerned with partially-overlapping stochastic block models, more useful tackling real-life problems. propose edge exploited profile method refined variations. conduct thorough analysis our proposed methods’ performances range challenging scenarios, including coauthorship data set zebrafish neuron activity set. Our methods proved be numerically superior than state-of-the-art methods. The implemented R (A language environment for statistical computing, Foundation Statistical Computing, Vienna, 2020) package GMPro (GMPro: profiles, 2020).