Abstract Leveraging on graph automorphic properties of complex networks (CNs), this study investigates three robustness aspects of CNs including the robustness of controllability, disturbance decoupling, and fault tolerance against failure in a network element. All these aspects are investigated using a quantified notion of graph symmetry, namely the automorphism group, which has been found implications for the network controllability during the last few years. The typical size of automorphism group is very big. The study raises a computational issue related to determining the whole set of automorphism group and proposes an alternative approach which can attain the emergent symmetry characteristics from the significantly smaller groups called generators of automorphisms. Novel necessary conditions for network robust controllability following a failure in a network element are attributed to the properties of the underlying graph symmetry. Using a symmetry related concept called determining set and a geometric control property called controlled invariant, the new necessary and sufficient conditions for disturbance decoupling are proposed. In addition, the critical nodes/edges of the network are identified by determining their role in automorphism groups. We verify that nodes with more repetition in symmetry groups of the network are more critical in characterizing the network robustness. Further, the impact of elimination of critical network elements on its robustness is analyzed by calculating a new improved index of symmetry which considers the orbital impacts of automorphisms. The importance of all symmetry inspired findings of this paper is highlighted via simulation on various networks.

中文翻译：

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复杂网络鲁棒性的图自守方法

摘要 本研究利用复杂网络 (CN) 的图自守特性，研究了 CN 的三个鲁棒性方面，包括可控性的鲁棒性、干扰解耦和网络元素故障的容错性。所有这些方面都使用图对称的量化概念进行研究，即自同构群，在过去几年中已经发现它对网络可控性有影响。自同构群的典型规模非常大。该研究提出了与确定整组自同构群相关的计算问题，并提出了一种替代方法，该方法可以从称为自同构生成器的显着较小的群中获得涌现对称特征。网络元素故障后网络鲁棒可控性的新必要条件归因于底层图对称性的属性。使用称为确定集的对称相关概念和称为受控不变量的几何控制特性，提出了新的扰动解耦的充分必要条件。此外，网络的关键节点/边是通过确定它们在自同构群中的角色来识别的。我们验证了在网络的对称组中具有更多重复的节点在表征网络鲁棒性方面更为关键。此外，通过计算考虑自同构的轨道影响的新的改进对称指数，分析了消除关键网络元素对其鲁棒性的影响。