多层复杂网络的抗毁性及其应用研究

The invulnerability models of multilayer network have shown its better performance in the global sea and air transportation networks, computer communication networks, wireless sensor network etc., meanwhile, it contributes to explaining the phenomenon that cannot be described by single network. Therefore, it is of great significance and practical value to research and design multilayer network system with strong invulnerability. Our research aims to exploring the invulnerability of multilayer complex networks and its applications including network modeling and property analysis, calculating and comparison for diverse invulnerability measurement, optimal network structure etc. First, we shall present some new description approaches for multi-dimensional and interdependent multilayer network models, and analyze its corresponding characteristics. Given the attack strategies of nodes or edges, we then research the characteristics of global anti-destroyed (e.g. network reliability) and local anti-destroyed (e.g. the number of subtrees, spanning trees, vertex-induced subgraphs) measurement for network models, we also provide some valid or approximate algorithms. Based on the proposed measurement characteristics, we deeply explore the characteristics of optimal structure in multilayer network and each single layer network using proposed different measurement algorithms in multilayer network, we then build an optimal multilayer network. We finally verify and analyze the invulnerability and its applications using our presented models and approaches in wireless sensor network. Our work also provides the theoretical basis and technical support for building optimal wireless sensor networks.

多层网络抗毁性模型已在全球海空联运网络、计算机通信网络、无线传感器网络等系统进行了验证，多层网络理论有助于解释单个网络无法刻画的现象。因此，如何设计具有较强抗毁性的多层网络具有重要的理论意义和应用价值。本项目拟对多层复杂网络的抗毁性及其应用进行研究，主要包括多层网络模型构建及特性分析、不同抗毁性测度度量、最优多层网络结构特性分析和构建等。首先，提出刻画多维型和依存型多层网络模型的新方法，并分析其特性；其次，给定点（边）攻击策略，研究网络模型的全局抗毁性测度（网络可靠度）和局部抗毁性测度（子树、生成树、点导出子图等数目）性质，并给出其有效算法或近似算法；然后，利用测度的性质，研究多层网络中各层几种测度最优网络结构与整体网络最优结构性质，构建最优多层网络；最后，利用研究的结果和方法分析无线传感器网络抗毁性及其应用，为构建最优的无线传感器网络提供理论依据与技术支撑。

课题《多层复杂网络的抗毁性及其应用研究》是国家自然科学基金委于2017年批准给予资助项目。课题预定研究起始时间为2018年1月至2021年12月，资助金额为40万元。本项目主要研究了多层复杂网络模型构建算法、网络拓扑指标特性分析、网络抗毁性等动力学行为以及理论研究结果在实证网络上的应用等。研究内容有多层复杂网络模型构建及其拓扑特性分析、点和边失效条件下，多层网络抗毁性度量指标以及不同度量指标之下较优抗毁性网络模型的确定、多层网络传播机制和社团结构、理论结果在实证多层网络中的应用等四个方面。课题组集中精力对多层网络模型构建及其抗毁性进行研究，完成预定研究内容的同时，发挥成员的优势和研究兴趣，适当扩充了超网络鲁棒性、多层网络传播机制和社团结构对网络抗毁性的影响以及网络表示算法等研究内容，共完成各类研究论文19篇，已发表论文17篇，完成硕士论文5篇，完成博士论文1篇。