Betweenness is a crucial measure to evaluate the significance of the nodes and link in the networks, which is widely used in centrality ordering, failure cascading modeling and path planning. However, we have very little knowledge about the betweenness, which prevents the deep analysis. In this paper, we discovered two betweenness identities, which represent that the node and link betweenness is closely relative to the average length of the shortest paths in the network. Betweenness distribution is a globally parameter and uniquely determines the small-world property of the network.

Due to the sharing and open‐access characteristics of the wireless medium, wireless sensor networks (WSNs) can be easily attacked by jammers. To mitigate the effects of a jamming attack, one reliable solution is to locate and remove the jammer from the deployed area within the WSN. To realize the jammer’s localization in the WSN, many range‐free methods have been proposed. However, most of these methods are sensitive to the distribution of nodes and the parameters of the jammer. For this reason, a jammer location‐aware method based on Fibonacci branch search (FBS) is proposed in this article. First, the interference region is estimated by using the interference region mapping service of sensors in wireless sensor networks. Then, the search point is selected in the jamming area and the fitness function is designed according to the average distance from the search point to the boundary sensor. According to the basic branch structure and interactive search rules, the global optimal solution is obtained in the jamming area. Finally, the position of the search point with the best fitness value is used as the estimation of the jammer position. Compared with the existing typical range‐free methods, rich simulation experiments demonstrate that the FBS algorithm is superior in the location‐aware method for jammers with a higher precision and a lower sensitivity to the distribution of nodes and the parameters of the jammer, respectively.

In the field of maritime safety research, ship behavior analysis is usually based on data provided by automatic identification systems (AISs). Prevailing studies predominantly focus on detecting the behaviors of vessels that may affect maritime safety, especially the abnormal disappearance of ship AIS signals, neglecting subsequent measures to trace these illegal ships. To fill this gap, we propose a deep learning model named multi-dimensional convolutional long short-term memory (MConLSTM) to tackle the challenge of recognizing ship trajectories in cases where AIS signals are intentionally altered. By employing a self-supervised approach, the model is trained using historical real-world data. Extensive experiments show that MConLSTM exhibits superior analytical capabilities when it comes to processing and analyzing AIS data. Notably, even in scenarios with scant training data, the model exhibits exceptional performance, with an average accuracy 22.74% higher than the general model. Finally, we validated the practical significance and feasibility of the proposed method by simulating real-world scenarios.