![]() ![]() LVD uses the increasing rate of the sum of neighbor nodes’ degrees in a node’s box with the logarithm of box size to assess a node’s importance. Based on this principle, LD adopts the concept of the boxing covering method and considers that the increasing rate of the total number of neighbor nodes in a node’s box with its size reflects the importance of the node. In complex networks, the neighbors of a node are the key factor to its importance. Furthermore, centrality measures based on bionics algorithm, and k-shell decomposition method, are also put forward. proposed the ranking method of influential nodes in social networks by neighborhood diversity and neighborhood correlation coefficient. From the perspective of a node’s neighbors, Zareie et al. From the perspective of interactions between nodes, centrality methods based on gravity model, are proposed. Inspired by LD, researchers combined information theory with it and proposed Local Information Dimension (LID), Local Fuzzy Information Centrality (LFIC), Local Volume Dimension (LVD). Adopting the concept of the power law distribution of nodes’ degrees, a local dimension measure (LD) was proposed by Pu et al. These methods lay emphasis on different proporties of networks and have their respective advantages. In recent years, researchers have proposed many novel centrality measures based on different properties of complex networks. Degree centrality (DC), betweenness centrality (BC), closeness centrality (CC), eigenvector centrality (EC), PageRank are some of these classical centrality methods. Moreover, the identification of influential nodes in new network models has also attracted considerable attention.Īlthough there are some existing classical methods of the nodes’ importance assessment, they all have their own limitations and defects which lead to their unideal results in certain application scenarios. Thus, researches on the identification of influential spreaders in many fields are receiving widespread attention, such as epidemic control, social networks, , financial crisis detection and biological networks. The influential spreaders, essential tothe network’s structure and invulnerability, have critically important effects on many real-world complex systems. In recent years, how to mine the influential spreaders in complex networks has become a hot issue. As a result of the complex network’s wide application, various researches on it have attracted the attention of researchers, such as link prediction, , community detection, , the fractal dimension, ,, and identification of influential nodes. By transforming the research targets into nodes and relationships among them into edges, many real world systems, such as biological systems, , multi-criteria decision making, , social systems, , multi-agent systems, electrical power system and time series, can be depicted as complex networks. The research of complex networks is increasingly playing a prominent role in network science because of complex networks’ great and effective capability of modeling complex systems in real world. Experimental results show that LDD has a higher identification accuracy and a stronger ability to quantify node’s importance. To demonstrate the effectiveness of LDD, six experiments are conducted on six real-world complex networks. A node with a larger LDD value has a more significant impact on networks. LDD creatively combines the increasing rate and decreasing rate of the numbers of each layer neighbor nodes to obtain its Local Degree Dimension value, which is comprehensive and reasonable. Different from the existing work, LDD regards the numbers of central node’s each layer neighbor nodes as the basis of nodes’ importance calculation. In this paper, a Local Degree Dimension (LDD) approach to identify influential nodes in complex networks is proposed. However, they do not take the global information of networks into consideration. Among them, centrality measures based on local properties of nodes are widely used, which assess the importance of nodes based on their degrees. Many centrality measures, each has its own emphasis, have been put forward by researchers. How to identify influential nodes is still an urgent and crucial issue of many researches on complex networks. The importance of researches on complex networks is becoming more and more prominent.
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