Finding the set of nodes, which removed or (de)activated can stop the spread
of (dis)information, contain an epidemic or disrupt the functioning of a
corrupt/criminal organization is still one of the key challenges in network
science. In this paper, we introduce the generalized network dismantling
problem, which aims to find the set of nodes that, when removed from a network,
results in a network fragmentation into subcritical network components at
minimum cost. For unit costs, our formulation becomes equivalent to the
standard network dismantling problem. Our non-unit cost generalization allows
for the inclusion of topological cost functions related to node centrality and
non-topological features such as the price, protection level or even social
value of a node. In order to solve this optimization problem, we propose a
method, which is based on the spectral properties of a novel node-weighted
Laplacian operator. The proposed method is applicable to large-scale networks
with millions of nodes. It outperforms current state-of-the-art methods and
opens new directions in understanding the vulnerability and robustness of
complex systems.

本文介绍了广义网络拆除问题，并提出了基于新型节点加权拉普拉斯算子的方法，以解决拆除网络中节点将导致网络崩溃的问题。该方法适用于拥有数百万个节点的大型网络，优于现有技术，并开辟了了解复杂系统的脆弱性和稳健性的新途径。

通用网络拆解

Generalized Network Dismantling

We study the network dismantling problem, which consists in determining a
minimal set of vertices whose removal leaves the network broken into connected
components of sub-extensive size. For a large class of random graphs, this
problem is tightly connected to the decycling problem (the removal of vertices
leaving the graph acyclic). Exploiting this connection and recent works on
epidemic spreading we present precise predictions for the minimal size of a
dismantling set in a large random graph with a prescribed (light-tailed) degree
distribution. Building on the statistical mechanics perspective we propose a
three-stage Min-Sum algorithm for efficiently dismantling networks, including
heavy-tailed ones for which the dismantling and decycling problems are not
equivalent. We also provide further insights into the dismantling problem
concluding that it is an intrinsically collective problem and that optimal
dismantling sets cannot be viewed as a collection of individually well
performing nodes.

研究网络拆除问题，通过 随机图的解联通问题以及疾病传播理论得到最小的拆除集，使用 Min-Sum 算法有效的拆除网络并提出最优拆除集不是单个节点的问题。