Analytical results of the k-core pruning process on multiplex networks

Multiplex networks are generally considered as networks that have the same set of vertices but different types of edges. Multiplex networks are especially useful when describing systems with several kinds of interactions. In this paper, we study the analytical solution of the k-core pruning process on multiplex networks. k-Core decomposition is a widely used method to find the dense core of the network. Previously, the Non-Backtracking Expansion Branch (NBEB) has been found to be able to easily derive the exact analytical results in the k-core pruning process. Here, we further extend this method to solve the k-core pruning process on multiplex networks by designing a variation of the method called the Multicolor Non-Backtracking Expansion Branch (MNEB). Our results show that, given any uncorrelated multiplex network, the Multicolor Non-Backtracking Expansion Branch can offer the exact solution for each intermediate state of the pruning process.