Influential Nodes in the OBOR Fossil Energy Trade Network Based on D-S Theory: Detection and Evolution Analysis

The structure formed by fossil energy trade among countries can be divided into multiple subcommodity networks. However, the difference of coupling mode and transmission mechanism between layers of the multirelationship network will affect the measurement of node importance. In this paper, a framework of multisource information fusion by considering data uncertainty and the classical network centrality measures is build. Then, the evidential centrality (EVC) indicator is proposed, by integrating Dempster–Shafer evidence theory and network theory, to empirically identify influential nodes of fossil energy trade along the Belt and Road Initiative. The initial result of the heterogeneity characteristics of the constructed network drives us to explore the core node issue further. The main detected evidential nodes include Russia, Kazakhstan, Czechia, Slovakia, Egypt, Romania, China, Saudi Arabia, and Singapore, which also have higher impact on network efficiency. In addition, cluster analysis discovered that resource endowment is an essential factor influencing country’s position, followed by geographical distance, economic level, and economic growth potential. Therefore, the above aspects should be considered when ensuring national trade security. At last, the rationality and comprehensiveness of EVC are verified by comparing with some benchmark centralities.

Improved gravity model for identifying the influential nodes

Identifying the influential nodes in network is essential for network dynamic analysis. In this letter, inspired by the gravity model, we present an improved gravity model (EDGM) to identify the influential nodes in network through the effective distance. Firstly, we calculate the degree of nodes. Then we construct the effective distance combined with the interaction frequency between nodes, so as to establish the effective distance gravity model. Comparing with the susceptible-infected model, the results show that the Kendall' s $\tau$ correlation coefficient of EDGM could enhanced by 2.36\% for the gravity model. Compared with other methods, the Kendall' s $\tau$ correlation coefficient of EDGM could enhanced by 11.55%, 17.29%, 7.17% and 10.00% for the degree centrality, betweenness centrality, eigenvector centrality, and PageRank respectively. The results show that the improved gravity model could effectively identify the influential nodes in network.

A novel method for identifying influential nodes in complex networks based on gravity model

How to identify influential nodes in complex networks is an essential issue in the study of network characteristics. A number of methods have been proposed to address this problem, but most of them focus on only one aspect. Based on the gravity model, a novel method is proposed for identifying influential nodes in terms of the local topology and the global location. This method comprehensively examines the structural hole characteristics and K-shell centrality of nodes, replaces the shortest distance with a probabilistically motivated effective distance, and fully considers the influence of nodes and their neighbors from the aspect of gravity. On eight real-world networks from different fields, the monotonicity index, susceptible-infected-recovered (SIR) model, and Kendall's tau coefficient are used as evaluation criteria to evaluate the performance of the proposed method compared with several existing methods. The experimental results show that the proposed method is more efficient and accurate in identifying the influence of nodes and can significantly discriminate the influence of different nodes.