Using NonBacktracking Expansion to Analyze k-core Pruning Process

We induce the NonBacktracking Expansion Branch method to analyze the k-core pruning process on the monopartite graph G which does not contain any self-loop or multi-edge. Different from the traditional approaches like the generating functions or the degree distribution evolution equations which are mathematically difficult to solve, this method provides a simple and intuitive solution of the k-core pruning process. Besides, this method can be naturally extended to study the k-core pruning process on correlated networks, which is among the few attempts to analytically solve the problem.