Random node reinforcement and K-core structure of complex networks

To enhance robustness of complex networked systems, a simple method is introducing reinforced nodes which always function during failure propagation. A random scheme node reinforcement can be considered as benchmark for finding an optimal solution. Yet there still lacks systematic evaluation on how affects network structure at mesoscopic level upon failures. Here we study this problem through the lens K-cores networks. Based analytical percolation framework, first show that, uncorrelated graphs, with critical size nodes, abrupt emergence smoothed out to continuous one, and detailed phase diagram derived. We then cost–benefit analysis reinforcement, proper weight factors in cost functions constant increasing marginal costs, gain shows unimodality, thus analytically find fraction by locating maximal gain. In all, our framework offers gain-oriented perspective designing robust interconnected systems.