时序网络的鲁棒性、可修复度与时间关联

Robustness has been a major topic of network theory. The key point is to investigate the critical threshold of network robustness under internal or external failures. Static robustness is not adequate to capture all aspects of temporal networks since it does not take into account time-dependent connections. It becomes important to develop a robustness metric that incorporates the temporal dimension and gives insights on how temporal network is affected by damage or change. With the concern that current study of temporal robustness only contains topological analyses, we are aimed at designing a framework of temporal robustness and repairability by integrating the spreading dynamics. Our research can be conducted as follows. First, investigate temporal robustness based on spreading ability and topological centrality, respectively. Second, evaluate the repair strategy qualitatively and quantitatively by applying the constraints of time-respected paths and rapidly-changing topologies. Third, compare the correlation properties before and after the error and attack as well as the repair with the performance of Temporal Null Model (TNM), Detrended Fluctuation Analysis (DFA) and Factorial Moments (FM). The result can help to reveal the influence of temporal correlations and spreading dynamics on temporal networks from a new respective. This project is of significance for locating the critical threshold of robustness and repairability and emphasizing the temporal effects; and for designing and protecting important complex systems.

鲁棒性是网络科学的一个重要研究方向。探寻复杂网络在内部故障与外部干扰下的鲁棒性临界条件是研究的关键问题。大数据背景下静态网络已不足以刻画真实的复杂系统，提出基于时间信息的鲁棒性研究至关重要。注意到当前时序网络的鲁棒性分析主要借助静态网络结构开展，没有充分体现时间特征的影响，提出结合时间关联与传播动力学过程建立时序网络鲁棒性与修复研究的基本框架。项目将从三个方面展开：首先，分别依据节点传播能力和拓扑结构中心性识别关键节点，研究时序网络在出错与遭袭下的鲁棒性；其次，考虑路径时序的限制与系统快速变化的时间特征，定性评估和定量计算时序网络的修复程度与依赖条件；第三，利用零模型、DFA、阶乘矩等方法，研究对比时序网络在出错与遭袭前后、修复前后的时间关联，从新的角度揭示时序网络的关联特征。研究结果不仅有助于明确时序网络鲁棒性与修复程度的临界现象，强调时间特征的影响，也有助于保护和设计重要的复杂系统。

鲁棒性评估对网络的设计和维护至关重要，项目旨在结合时间关联与传播动力学过程探讨时序网络鲁棒性与修复研究的基本框架。一方面，引入传播概率、传播时间等参量，通过分析时序网络上的疾病传播模型，发现节点的传播能力、传播效率、传播阈值等均可以作为识别关键节点的指标，其中时序度最能体现时序网络的节点重要性。其次，构建时序网络在遭受攻击后的不同修复策略，提出修复成本的概念用以衡量时序网络的传播能力与修复效率，结果表明依据时序度对节点进行修复，其成本最低，效率最高。最后，引入节点的适应度，关注时间特性对每一个节点在传播中的作用，研究发现局域拓扑结构比全局阈值对节点的传播限制更大。项目的研究不仅有助于识别时序网络的鲁棒性特征、掌握时序网络的修复行为，也有助于理解时间关联在复杂网络中的重要作用。