Graph matching beyond perfectly-overlapping Erdős-Rényi random graphs

Yaofang Hu, Wanjie Wang, Yi Yu

Abstract: 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, which was previously used only in noiseless graphs and perfectly-overlapping Erdős–Rényi 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).