Core Percolation in Coupled Networks

Core percolation is crucial in network controllability and robustness. Prior works are mainly based on single, non-interacting network where core nodes are obtained by a classic Greedy Leaf Removal (GLR) procedure that takes of leaf nodes along with their neighbors iteratively. We take a first look into core percolation in coupled networks with two fully-interdependent networks. To obtain core nodes in both networks, we propose a new algorithm, called Alternating GLR procedure, that recursively switches between networks in carrying out GLR for node removal. We prove that the proposed algorithm can guarantee the uniqueness in the sense that the final remaining nodes and edges in either of the coupled networks remain the same, and then present analytical solutions for the fraction of core nodes that will be ultimately left when the algorithm terminates. Our simulation demonstrates that the presence of core exhibits a jump at the critical point as a first order transition in coupled networks.