As a classical trade model, the gravity model plays an important role in the trade policy-making process. However, the effect of physical distance fails to capture the effects of globalization and even ignores the multilateral resistance of trade. Here, we propose a general model describing the effective distance of trade according to multilateral trade paths information and the structure of the trade flow network. Quantifying effective trade distance aims to identify the hidden resistance information from trade networks data, and then describe trade barriers. The results show that flow distance, hybrid by multi-path constraint, and international trade network contribute to the forecasting of trade flows. Meanwhile, we also analyze the role of flow distance in international trade from two perspectives of network science and econometric model. At the econometric model level, flow distance can collapse to the predicting results of geographic distance in the proper time lagging variable, which can also reflect that flow distance contains geographical factors. At the international trade network level, community structure detection by flow distances and flow space embedding instructed that the formation of international trade networks is the tradeoff of international specialization in the trade value chain and geographical aggregation. The methodology and results can be generalized to the study of all kinds of product trade systems.

Network embedding is a frontier topic in current network science. The scale-free property of complex networks can emerge as a consequence of the exponential expansion of hyperbolic space. Some embedding models have recently been developed to explore hyperbolic geometric properties of complex networks—in particular, symmetric networks. Here, we propose a model for embedding directed networks into hyperbolic space. In accordance with the bipartite structure of directed networks and multiplex node information, the method replays the generation law of asymmetric networks in hyperbolic space, estimating the hyperbolic coordinates of each node in a directed network by the asymmetric popularity-similarity optimization method in the model. Additionally, the experiments in several real networks show that our embedding algorithm has stability and that the model enlarges the application scope of existing methods.

Feature selection is a crucial step in fault diagnosis. When rolling bearings are susceptible to compound faults, causal relationships are hidden within the signal features. Complex network analysis methods provide a tool for causal relationship modeling and feature importance assessment. Existing studies mainly focus on unweighted networks, overlooking the impact of the strength of causal relationships on feature selection. To address this issue, we propose a compound fault feature selection method based on the causal feature weighted network. First, we construct a weighted network using the incremental association Markov blanket discovery algorithm and Pearson correlation coefficient. Then, we quantify the importance of features by treating node strength as a centrality index and rank them to partition the feature subset. Finally, the optimal feature subset is obtained through a neural network with the accuracy of compound fault diagnosis as the threshold. Analysis of public datasets and comparative experiments demonstrate the advantages of our method. Compared to existing research, our method not only effectively reduces the number of optimal feature subsets to 11 but also improves the accuracy of compound fault diagnosis to 95.2%. Furthermore, we employ the SHapley Additive exPlanations to interpret the contribution of each feature in the optimal subset to the accuracy of compound fault diagnosis. This provides reference from both physical and network perspectives to feature selection and compound fault diagnosis in rolling bearings in practical working conditions.

A rolling bearing is a complex system consisting of the inner race, outer race, rolling element, etc. The interaction of components may lead to composite faults. Selecting the features that can accurately identify the fault type from the composite fault features with causality among components is key to composite fault diagnosis. To tackle this issue, we propose a feature selection approach for composite fault diagnosis based on the causal feature network. Based on the incremental association Markov blanket discovery, we first use the algorithm to mine the causal relationships between composite fault features and construct the causal feature network. Then, we draw upon the nodes’ centrality indicators in the complex network to quantify the importance of composite fault features. We also propose the criteria for threshold selection to determine the number of features in the optimal feature subset. Experimental results on the standard dataset for composite fault diagnosis show that our approach of using the causal relationship between features and the nodes’ centrality indicators of complex network can effectively identify the key features in composite fault signals and improve the accuracy of composite fault diagnosis. Experimental results thus verify our approach’s effectiveness.

The phenomenon of load redistribution in complex networks has garnered extensive attention due to its profound impact and widespread occurrence. In recent years, higher-order structures have offered new insights into understanding the structures and dynamic processes of complex networks. However, the influence of these higher-order structures on the dynamics of load redistribution, cascade failures, and recovery processes remains to be fully explored. In this study, we propose the load redistribution model with higher-order structures and recovery strategies of cascade failure based on functional upgrading and reconstruction mechanisms. In the cascading failure process with load redistribution and higher-order recovery strategies, we find that higher-order structures can induce a discontinuous phase transition at the low proportion of load redistribution, and the dynamic process displays a dual character of being robust yet fragile. These findings have been examined in both real and classical modeled networks. Interestingly, the largest connected component exhibits three distinct modes as the attack ratio increases at high densities of higher-order structures and recovery mechanisms.

Global trade including energy trade is expected to suffer a significant contraction as a result of the COVID-19 pandemic. In this paper, we try to measure the impact of the COVID-19 pandemic on the national status and international energy trade patterns. We apply the networks theory to quantify the dynamic process of the international energy trade network in the year 2018–2020, deriving the $\mathrm{\Omega }$ centrality to capture both national economic status and its topologic characteristics. Under the COVID-19, multilateral energy trade was blocked, thereby some resource-exporting countries show a downward rank of the $\mathrm{\Omega }$ centrality, and the opposite situation is in higher levels of economic development. By using the community detection method, we also found that new small communities detached from communities that formed before the COVID-19, but geographical related patterns of international energy trade network communities were not affected by the COVID-19 pandemic.