Network resilience: impact on small-world network

Lots of complex systems in the real world have network structures, and a number of these structures have small-world property. This kind of structures are called small-world networks. Examples include the world's air transportation system, electric power systems, and human functional brain network, and small-world property is one of the key reasons why these systems function efficiently. However, for complex systems, in addition to their efficiency, resilience or robustness is also one of the concerns, as these systems need to ensure that they do not completely collapse on their own in case of failure of a small number of their components. The purpose of this paper is to try to find and explain the factors that affect the robustness of small-world network by comparing different classes of small-world networks and analysing differences between them and possible causes of these differences, in order to get an idea to optimize the robustness of small-world networks while preserving their small-world property.