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.

Cascading failures in the command and control networks (C2 networks) could substantially affect the network invulnerability to some extent. In particular, without considering the characteristics of hierarchy structure, it is quite misleading to employ the existing cascading failure models and effectively analyze the invulnerability of C2 networks. Therefore, a novel cascading failure model for command and control networks with hierarchy structure is proposed in this paper. Firstly, a method of defining the node's initial load in C2 networks based on hierarchy-degree is proposed. By applying the method, the impact of organizational positions and the degree of the node on its initial load could be highlighted. Secondly, a nonuniform adjustable load redistribution strategy (NALR strategy) is put forward in this paper. More specifically, adjusting the redistribution coefficient could allocate the load from failure nodes to the higher and the same level neighboring nodes according to different proportions. It could be demonstrated by simulation results that the robustness of C2 networks against cascading failures could be dramatically improved by adjusting the initial load adjustment coefficient, the tolerance parameter, and the load redistribution coefficient. And finally, comparisons with other relational models are provided to verify the rationality and effectiveness of the model proposed in this paper. Subsequently, the invulnerability of C2 networks could be enhanced.

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In this study, a novel direct Z-scheme SnS2 quantum dots/sulfur-doped polyimide (SQDs/SPI) photocatalyst was firstly fabricated by an in situ crystallization growth of SnS2 quantum dots on sulfur-doped polyimide through a facile hydrothermal method. The photocatalytic hydrogen production activity of 5SQDs/SPI samples reached 3526 μmoL g−1 in the coexistence of triethanolamine and methanol used as hole sacrificial agents, which is about 13 times higher than that of SPI under the same conditions and 42 times higher than that of SPI only as a hole sacrificial agent. The improvement can be related to the direct Z-scheme charge transfer in the tight interface between SQDs and SPI, which promoted rapid separation and significantly prolonged the lifetime of photoexcited carriers. The Z-scheme charge transfer mechanism was proposed. This discovery comes up with a new strategy for the development of an efficient, environmentally friendly, and sustainable sulfide quantum dots/polymer non-noble metal photocatalyst.

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