spread of the virus. For another example, [PERSON] et al. collected 20 years of trade data from 232 countries and regions around the world, and then constructed a trade network. In this network, a novel node importance ranking and analysis method was proposed by comprehensively considering factors such as generalized degree, DHC theorem and weight [10]. This method helps the formulation of trade policies in countries around the world, and deepens our understanding of the history of world trade. [PERSON] et al. also pointed out that for traditional information retrieval evaluation metrics based on citation network structure, it is difficult to accurately assess the impact of a particular piece of literature. They experimentally argued that the adapted PageRank and LeaderRank methods are still the most accurate evaluation criteria available [11]. As an interdisciplinary subject, there are examples of applying various computer technologies to the research of complex networks. For example, [PERSON] et al. proposed an artificial neural network-based model for information dissemination and opinion evolution, IPNN (Information propagation and public opinion evolution model based on artificial neural network, IPNN) [12]. [PERSON] et al. proposed a reinforcement learning-based algorithm for node importance identification in complex networks, FINDER. It first learns the exhaustive method in a simulated BA network, continues training the previously trained model in the real network, and evaluates the performance of the model based on the order of node removal [13]. In addition, many excellent improvements to the traditional node importance recognition algorithm have also been proposed. For example, [PERSON] et al. proposed a new node importance ranking metric, the circle ratio, beginning from a circular structure in the network [14]. Traditional methods judge the importance of a node by the contributions of neighboring nodes. However, the circle ratio judges the importance of the current node by the amount of information it brings to its neighbors, which inspires a new research idea [14]. [PERSON] and [PERSON] et al. summarized and sorted out the current node importance identification and ranking methods in various existing networks [15; 16]. As we can see, most of the current research on nodes focuses on the mining and discovery of important nodes in a network, but little research exists on the mining of relatively important nodes. The idea of relative node importance considers questions like \"which node in a network is the most important relative to a specific node or a specific group of nodes?\" Compared with other research fields, the relative or local importance of nodes also has practical implications, especially when the scale of the network grows larger. Some research results on relative node importance mining are available today, but these methods still need improvement. Areas of improvement include whether the time complexity and space complexity can be further reduced, how to further improve the accuracy of exiting method, which kind of method performs the best on a specific type of network, and the parameter selection and optimization method, etc. In this paper, we consider the connection role of important edges in an unweighted network, where the edge importance represents the degree of association between two nodes. The connections between important nodes should be closer, thus we propose a metric to measure edge closeness for important nodes in an unweighted network. It is based on the idea of \"the node with the largest edge closeness to a known important node is likely to be an important node\" for which an edge importance greedy strategy (EG) is proposed to mine relatively important nodes.