Improving measures of topological robustness in networks of networks and suggestion of a novel way to counter both failure propagation and isolation

The study of interdependent complex networks in the last decade has shown how cascading failure can result in the recursive and complete fragmentation of all connected systems from the destruction of a comparatively small number of nodes. Existing "network of networks" approaches are still in infancy and have shown limits when trying to model the robustness of real-world systems, due to simplifying assumptions regarding network interdependencies and post-attack viability. In order to increase the realism of such models, we challenge such assumptions by validating the following four hypotheses through experimental results obtained from computer based simulations. Firstly, we suggest that, in the case of network topologies vulnerable to fragmentation, replacing the standard measure of robustness based on the size of the one largest remaining connected component by a new measure allowing secondary components to remain viable when measuring post-attack viability can make a significant improvement to the model. Secondly, we show that it is possible to influence the way failure propagation is balanced between coupled networks while keeping the same overall robustness score by allowing nodes in a given network to have multiple counter parts in another network. Thirdly, we challenge the generalised assumption that partitioning between networks is a good way to increase robustness and that isolation is a force as equally destructive as the iterative propagation of cascading failure. This result significantly alters where the optimum robustness lies in the balance between isolation and inter-network coupling in such interconnected systems. Finally, we propose a solution to the consequent problem of seemingly ever increasing vulnerability of interdependent networks to both cascading failure and isolation: the use of permutable nodes that would give such systems rewiring capabilities. This last concept could have wide implications when trying to improve the topological resilience of natural or engineered interdependent networks.