Current command and control (C2) network models typically do not account for differences in attributes of nodes that belong to the same class; in addition, there is no provision in these models for adequate description of operational relationships that exist between multiple combat entities with different attributes in real-world scenarios. To address these issues, we propose a method to model multilevel command and control supernetworks (MC2S) based on attribute synergy prioritization and hypergraph theory. First, the characteristics of C2 supernetworks are analyzed to abstract their nodes and hyperedges, based on which, we propose the MC2S model, which consists of three layers and five networks. Second, the Term Frequency–Inverse Document Frequency (TF-IDF) and spatial distance algorithms are used to construct an attribute synergy prioritization-based strategy for the generation of intra-layer MC2S hyperedges, while local-world (LW) selection is used to create an LW model-based method for the generation of inter-layer MC2S hyperedges. Through simulation experiments, we show that our model exhibits (approximately) scale-free properties as well as small-world properties, excellent cooperative engagement capabilities (CEC), and has a high level of network invulnerability. These findings will serve as a useful reference for the description of complex nodal (edge) relationships in C2 networks, network performance analyses, and deployment of complex combat mission networks.

Statistical correlation analysis is currently the most typically used approach for investigating the risk factors of type 2 diabetes mellitus (T2DM). However, this approach does not readily reveal the causal relationships between risk factors and rarely describes the causal relationships visually. Considering the superiority of reinforcement learning in prediction, a causal discovery approach with reinforcement learning for T2DM risk factors is proposed herein. First, a reinforcement learning model is constructed for T2DM risk factors. Second, the process involved in the causal discovery method for T2DM risk factors is detailed. Finally, several experiments are designed based on diabetes datasets and used to verify the proposed approach. The experimental results show that the proposed approach improves the accuracy of causality mining between T2DM risk factors and provides new evidence to researchers engaged in T2DM prevention and treatment research.

The DR-SCIR network public opinion propagation model was employed to study the characters of S-state users stopping transmitting information for the first time and secondary transmission of immune users. The model takes into account symmetry and complexity such as direct immunization and social reinforcement effect, proposes the probability of direct immunity Psr and the probability of transform from the immune state to the hesitant state Prc, and divides public opinion information into positive public opinion and negative public opinion based on whether the public opinion information is confirmed. Simulation results show that, when direct immunity Psr = 0.5, the density of I-state nodes in the model decreased by 54.12% at the peak index; when the positive social reinforcement effect factor b = 10, the density of I-state nodes in the model increased by 16.67% at the peak index; and when the negative social reinforcement effect factor b = -10, the density of I-state nodes in the model decreased by 55.36% at the peak index. It shows that increasing the positive social reinforcement effect factor b can promote the spread of positive public opinion, reducing the negative social reinforcement effect factor b can control the spread of negative public opinion, and direct immunization can effectively suppress the spread of public opinion. This model can help us better analyze the rules of public opinion on social networks, so as to maintain a healthy and harmonious network and social environment.

Formation coordination can improve the overall performance of unmanned aerial vehicle (UAV) systems, so it is important to realize coordinated formation control. To solve the problems of ineffective internal collision avoidance and communication distance maintenance in existing formation control methods, a UAV formation control algorithm based on an improved artificial potential field and consensus is proposed. First, an improved artificial potential field obstacle avoidance method is used to solve the problems of collision avoidance and communication distance maintenance within the formation by setting a communication risk zone and a collision risk zone and by defining the dynamic adjustment parameters of the inter‐UAV virtual force to improve the traditional artificial potential field method. Second, a time integrating factor is introduced, and an improved consensus‐based formation control method is employed to overcome the problem of the artificial potential field method falling into the local optimum easily. Simulation experiments were designed to analyse the trends of the UAV formation motion trajectory, inter‐UAV relative distance, attitude, and formation time. The analysis results show that the method can make the UAV formation consistent with the flight trajectory of the intended formation, solving the problems of collision avoidance and communication distance maintenance within the UAV formation.

Cascading failure models for command and control networks (C2 networks) continue to be a challenging and important research area. Current solutions share a common limitation because the solutions focus only on the importance of each node in isolation using one index rather than considering the contribution degree of neighboring nodes, which makes the initial load definition inaccurate and affects the cascading invulnerability of the network. To address this limitation, a new cascading failure model for C2 networks is proposed. The new model CFM_AdjM, which is based on an m-order adjacency matrix, proposes a method of initial load definition using the contribution degree of m-order neighboring nodes and defines the nonlinear load capacity model according to the nonlinear relationship between load and capacity. Finally, the influence of model parameters on the cascading failure of C2 networks is analyzed through simulation, and the results demonstrate that the new model effectively resists the cascading failure and enhances the survivability of the network by defining the initial load and adjusting the coefficient appropriately.

Influential nodes act as a hub for information transmission in a command and control network. The identification of influential nodes in a network of this nature is a significant and challenging task; however, it is necessary if the invulnerability of the network is to be increased. The existing k-shell method is problematic in that it features a coarse sorting granularity and does not consider the local centrality of nodes. Thus, the degree of accuracy with which the influential nodes can be identified is relatively low. This motivates us to propose a method based on an integral k-shell to identify the influential nodes in a command and control network. This new method takes both the global and local information of nodes into account, introduces the historical k-shell and a 2-order neighboring degree, and refines the k-shell decomposition process in a network. Simulation analysis is carried out from two perspectives: to determine the impact on network performance when influential nodes are removed and to obtain the correlation between the integral k-shell value and its propagation value. The simulation results show that the integral k-shell method, which employs an algorithm of lower complexity, accurately identifies the influence of those nodes with the same k-shell values. Furthermore, the method significantly improves the accuracy with which the influential nodes can be identified.