Optimally Connected Hybrid Complex Networks with Windmill Graphs Backbone

The significance of the existing analysis methods in complex networks and easy access to the ever-increasing volume of information present the emergence of proposing new methods in various fields based on complex system ideas. However, these systems are usually faced with various random failures and intelligent attacks. Due to the nature of the components' behaviors, the occurrence of the failures and faults in their operations and the alteration of their topologies are the most important problems. Since the complex systems are usually used as the infrastructures of other networks, their robustness against failures and the adoption of suitable precautions are necessary. Moreover, the smallworld effect in most complex systems is one of the crucial structural features. The authors found that the relation between these two is not well-known and may even be in conflict in some networks. The main goal in this paper is to achieve an optimal topology by utilizing a robustness-oriented multiobjective trade-off optimization model(edge rewiring) to establish a peaceful relationship between the two requirements. By offering a proposed rewiring method with the small-world effect, which is called core-periphery Windmill property, the authors demonstrated that the generated networks are able to exhibit appropriate robustness even during intelligent attacks. The results obtained in terms of Windmill graphs are presented very good approximations to demonstrate the small-world effect. These graphs are used as the initial core in the construction of the optimized networks' topologies.