Graph matching beyond perfectly-overlapping Erdos-Renyi random graphs

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