AUTHOR=Wu Rui-Jie , Kong Yi-Xiu , Zhang Yi-Cheng , Shi Gui-Yuan 

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

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.1076314

DOI=10.3389/fphy.2022.1076314

ISSN=2296-424X

ABSTRACT=Multiplex networks are generally considered as the networks that have the same set of vertices but different types of edges. Multiplex networks are especially useful when describing the systems with several kinds of interactions. In this paper we study the analytical solution of $\textbf{k}$-core pruning process on multiplex networks. $k$-core decomposition is a widely used method to find the dense core of the network. Previously the Nonbacktracking Expand Branch (NBEB) is 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 $\textbf{k}$-core pruning process on multiplex networks by designing a variation of the method called Multicolor Nonbacktracking Expand Branch (MNEB). Our results show that, given any initial multiplex network, Multicolor Nonbacktracking Expand Branch can offer the exact solution for each intermediate state of the pruning process.