An evolutionary optimal network design to mitigate risk contagion

Many real-world networks increase interdependencies and this creates challenges for handling network risks like cascading failure. In this paper, we propose an evolutionary approach for designing optimal networks to mitigate network risks. In general there is usually a trade-off between risk contagion and risk sharing, and optimizing a network requires the selection of a proper fitness function. We use the maximum eigenvalue of the adjacency matrix of a network to control risk contagion. The evolutionary optimized networks are characterized as homogeneous networks where all nodes have, roughly speaking, the same degree. We also show that maximum eigenvalue can be used as the index of robustness against cascading failure. The network with smaller maximum eigenvalue has better robustness against cascading failure.