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).

图匹配在算法和理论方面都是一个富有成果的领域。给定两个图\(G_1 = (V_1, E_1)\)和\(G_2 = (V_2, E_2)\)，其中\(V_1\)和\(V_2\)在未知排列上相同或大部分重叠\ (\pi ^*\)，图匹配就是寻求正确的映射\(\pi ^*\). 在本文中，我们利用了度信息，该信息以前仅用于无噪声图和完全重叠的 Erdős-Rényi 随机图匹配。我们关注部分重叠图和随机块模型的图匹配，这在解决现实生活中的问题时更有用。我们提出了边缘利用度轮廓图匹配方法和两个改进的变体。我们对我们提出的方法在一系列具有挑战性的场景中的性能进行了彻底的分析，包括共同作者数据集和斑马鱼神经元活动数据集。我们的方法被证明在数值上优于最先进的方法。这些算法在 R（统计计算的语言和环境，R Foundation for Statistical Computing，Vienna，2020）包 GMPro（GMPro：