Graph matching is an extremely fruitful research area. ( 2005) constructed graphs based on texts relationship and developed a system for deciding whether a given sentence can be inferred from text by matching graphs. ( 2016) seek the alignment of protein-protein interaction networks in order to uncover the relationships between different species Haghighi et al. For instance, Narayanan and Shmatikov ( 2009) targeted at acquiring information from an anonymous graph of Twitter with the graph of Flickr as the auxiliary information Kazemi et al. In recent years, due to the advancements in collecting, storing and processing large volume of data, graph matching is going through a renaissance, with a surge of work on graph matching in different application areas. A correct matching would help to augment the connectivity information between the vertices, and hence improve the graph analysis. Graph matching seeks the mapping \(\pi ^*\) between the vertex sets \(V_1\) and \(V_2\). Given two graphs \(G_1 = (V_1, E_1)\) and \(G_2 = (V_2, E_2)\), it is assumed that \(V_1\) and \(V_2\) are the same or largely overlapped upon an unknown permutation \(\pi ^*\). Mathematically, the graph matching problem can be loosely stated as follows. In this paper, we do not distinguish these terms, nor the terms “graph” and “networks”, or “nodes” and “vertices”. Ullmann 1976), and interpreted as “graph matching”, “network alignment” and “graph isomorphism”. The research on graph matching can be traced back to at least 1970s (e.g. Graph matching has been an active area of research for decades. 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). Our methods are proved to be numerically superior than the state-of-the-art methods. ![]() 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. We propose the edge exploited degree profile graph matching method and two refined variations. We are concerned with graph matching of partially-overlapping graphs and stochastic block models, which are more useful in tackling real-life problems. In this paper, we exploit the degree information, which was previously used only in noiseless graphs and perfectly-overlapping Erdős–Rényi random graphs matching. 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 \(\pi ^*\). Graph matching is a fruitful area in terms of both algorithms and theories.
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