标题： 多层网络上k-core剪枝过程的分析结果 显示英文标题

标题： Analytical Results of k-core Pruning Process on Multi-layer Networks

摘要： 多层网络或多重网络通常被认为是具有相同顶点集但不同类型的边的网络。 当描述具有多种相互作用的系统时，多层网络特别有用。 在本文中，我们研究了多层网络上$\textbf{k}$-core 剪枝过程的解析解。 $k$-core 分解是一种用于寻找网络密集核心的广泛使用的方法。 以前发现非回溯扩展分支（NBEB）能够轻松地在$k$-core 剪枝过程中得出精确的解析结果。 在这里，我们进一步将此方法扩展到通过设计一种称为多色非回溯扩展分支（MNEB）的方法来解决多层网络上的$\textbf{k}$-core 剪枝过程。 我们的结果表明，给定任何初始多层网络，多色非回溯扩展分支可以为剪枝过程的每个中间状态提供精确解，这些结果不仅适用于不相关的网络，也适用于具有层间相关性或层内相关性的网络。 显示英文摘要

摘要： Multi-layer networks or multiplex networks are generally considered as the networks that have the same set of vertices but different types of edges. Multi-layer 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 multi-layer 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 multi-layer networks by designing a variation of the method called Multicolor Nonbacktracking Expand Branch (MNEB). Our results show that, given any initial multi-layer network, Multicolor Nonbacktracking Expand Branch can offer the exact solution for each intermediate state of the pruning process, these results do not only apply to uncorrelated network, but also apply to networks with either interlayer correlations or in-layer correlations.