# Generalized Network Dismantling

arXiv: https://arxiv.org/abs/1801.01357 · HTML: https://mlsanity.com/paper/1801.01357/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2018.

## Built on by (most cited first, 13 of 13)

- [Machine learning dismantling and early-warning signals of disintegration in complex systems](https://mlsanity.com/paper/2101.02453/) (2021)
- [Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise](https://mlsanity.com/paper/2312.05974/) (2023)
- [Identify Critical Nodes in Complex Network with Large Language Models](https://mlsanity.com/paper/2403.03962/) (2024)
- [A Fast Algorithm for Moderating Critical Nodes via Edge Removal](https://mlsanity.com/paper/2309.06392/) (2023)
- [Recovering the Graph Underlying Networked Dynamical Systems under Partial Observability: A Deep Learning Approach](https://mlsanity.com/paper/2208.04405/) (2022)
- [Influential Simplices Mining via Simplicial Convolutional Network](https://mlsanity.com/paper/2307.05841/) (2023)
- [Hypernetwork Dismantling via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.14332/) (2021)
- [Advancing network resilience theories with symbolized reinforcement learning](https://mlsanity.com/paper/2507.08827/) (2025)
- [Promoting Fairness in Information Access within Social Networks](https://mlsanity.com/paper/2512.14711/) (2025)
- [Mastering Percolation-like Games with Deep Learning](https://mlsanity.com/paper/2305.07687/) (2023)
- [A Quick Framework for Evaluating Worst Robustness of Complex Networks](https://mlsanity.com/paper/2403.00027/) (2024)
- [Learning Network Dismantling Without Handcrafted Inputs](https://mlsanity.com/paper/2508.00706/) (2025)
- [Network World Models as Environments for Algorithm Design on Complex Systems](https://mlsanity.com/paper/2610.01048/) (2026)

## Abstract (arXiv)

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.