Evolution of correlated multiplexity through stability maximization

Investigating relation between various structural patterns found in real-world networks and stability of underlying systems is crucial to understand importance and evolutionary origin of such patterns. We evolve multiplex networks, comprising of anti-symmetric couplings in one layer, depicting predator-prey relation, and symmetric couplings in the other, depicting mutualistic (or competitive) relation, based on stability maximization through the largest eigenvalue. We find that the correlated multiplexity emerges as evolution progresses. The evolved values of the correlated multiplexity exhibit a dependence on the inter-link coupling strength. Furthermore, the inter-layer coupling strength governs the evolution of disassortativity property in the individual layers. We provide analytical understanding to these findings by considering star like networks in both the layers. The model and tools used here are useful for understanding the principles governing the stability as well as importance of such patterns in the underlying networks of real-world systems.