Source-linked AI summary
Generalized Network Dismantling
Xiao-Long Ren, Niels Gleinig, Dirk Helbing, Nino Antulov-Fantulin
TL;DR
Network dismantling seeks to stop harmful spreading processes or disrupt dysfunctional organizations by removing nodes at minimum cost, but conventional formulations assume equal node-removal costs. The paper introduces a generalized minimum-cost formulation and a spectral method based on a node-weighted Laplacian, reporting stronger performance than state-of-the-art methods for non-unit costs and better or comparable performance for unit costs.
Problem
Network dismantling must identify nodes whose removal fragments a network into subcritical components while addressing the limitation that conventional methods assume equal removal costs.
Method
The method combines a node-weighted Laplacian with randomized spectral approximations and weighted vertex-cover approximations to solve generalized dismantling problems with non-unit costs.
Results
The approach outperforms current state-of-the-art methods for non-unit costs and performs better or comparably for unit costs.
Takeaways & Limitations
Realistic costs based on node price, protection level, or other non-topological properties can be incorporated into cost-efficient network dismantling.
Takeaways & Limitations
Applications must be restricted to legitimate uses and actors because dismantling strategies can be misused, including for censorship when containing misinformation.
Abstract
from arXiv · showhide
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.
Significance Statement
The paper frames network dismantling as a way to disrupt harmful contagion and dysfunctional systems by removing or deactivating selected nodes. It introduces a framework that accounts for realistic removal costs and discusses applications to epidemics, criminal networks, corruption, and misinformation.
- Removing or deactivating selected nodes can fragment socio-technical networks, disrupting malfunctioning systems or containing misinformation and epidemics.
- The generalized framework incorporates realistic costs such as node price, protection level, and removal energy.
- Applications include cost-efficient dismantling strategies for epidemic spread, criminal networks, and corruption networks.
Main Contributions
The paper generalizes network dismantling to arbitrary non-negative node-removal costs and develops spectral, scalable approximations for solving the resulting optimization problem. On real networks, the approach outperforms state-of-the-art methods for non-unit costs and performs better or comparably for unit costs.
- The generalized problem finds a minimum-cost node set that fragments a network into components of subcritical size, allowing arbitrary non-negative removal costs.
- A node-weighted graph-cut objective provides an upper bound on generalized dismantling cost and has an analytical solution linked to a node-weighted Laplacian.
- The proposed Power Laplacian spectral approximation has complexity O(n·log2+ϵ(n)) and is supplemented by analytical bounds, convergence proofs, and weighted vertex-cover fine-tuning.
- On real networks, the approach outperforms current state-of-the-art methods for non-unit costs and performs better or comparably under unit costs.
Generalized network dismantling problem
The generalized network dismantling problem seeks a minimum-cost node set that fragments a network into components no larger than C, allowing arbitrary non-negative node-removal costs. The proposed method combines node-weighted spectral partitioning, a Power Laplacian approximation, recursive fragmentation, and weighted-vertex-cover fine-tuning.
- A C-dismantling set is a node subset whose removal leaves every connected component with at most C nodes.
- Unlike standard formulations with identical removal costs, the generalized problem assigns each node an arbitrary non-negative cost wi.Costs may represent removal energy, monetary control cost, node importance, or influence; unit costs recover the standard problem.
- Node-weighted spectral cut.: The node-weighted spectral objective assigns crossing edge (i, j) the removal cost wi + wj −1 and assigns zero cost to edges within a cluster.The degree centrality is used as a proxy for node weight when no other information is available.
- Node-weighted spectral cut.: The cost-weighted adjacency matrix B and Laplacian Lw encode the objective through B = AW + WA − A and Lw = DB − B.
- Node-weighted spectral cut.: The spectral relaxation uses the second-smallest eigenvector of Lw to split the network, then recursively applies the cut until components have maximum size C.Nodes with non-negative spectral entries adjacent to negative-entry nodes are removed to separate the two subnetworks.
- Spectral approximation.: The Power Laplacian approximation uses a shifted operator with the same eigenvectors as Lw and recursively achieves complexity O(n · log2+ϵ(n)) for sparse networks.The approximation converges toward an eigenvector associated with λ2; the method also provides spectral bounds and convergence results.
- For degree-proportional costs, GND and GNDR significantly outperform current state-of-the-art strategies across crime, corruption, information, and online social networks.On Pokec, containing 1.63 ∗106 nodes and 2.23 ∗107 edges, comparisons are limited to Min-Sum, BPD, and CoreHD because of other methods' scalability issues.
- Spectral approximation.: Fine-tuning solves a weighted vertex-cover problem on the subgraph of separating edges, with an efficient solution costing at most twice the optimal fine-tuning cost.
Results
Across real-world networks, GND and GNDR achieve target fragmentation at lower or comparable costs than existing dismantling strategies under non-unit and unit costs. The approach also incorporates realistic node costs, such as airport passenger flux, to model practical interventions.
- 0.2 versus 0.4: GND reaches 80% GCC size on Petster-hamster at half the cost of the Min-Sum comparison.
- 0.03 versus 0.1: GNDR reaches 50% GCC size on the crime network at lower cost than Min-Sum.
- 0.14 versus 0.19: GNDR reaches 50% GCC size on the corruption network at lower cost than Min-Sum.
- 0.55 versus 0.65 and 0.69 versus 0.91: GND or GNDR lowers the cost of 50% GCC fragmentation on information and online networks.
- For complete dismantling at approximately 1% of the original GCC size, GND approaches provide better or comparable solutions under unit costs.
- 0.06 versus 0.25: GND dismantles the world airport network to 80% GCC size using passenger-flux costs, compared with Min-Sum.
Conclusion
The paper presents generalized network dismantling as a cost-effective framework for fragmenting networks under realistic node costs, while highlighting ethical constraints on its use. It identifies applications in robustness and containment but warns that misuse can undermine network functionality and public discourse.
- Generalized network dismantling seeks to fragment networks into subcritical components at minimum cost while allowing unequal node-removal costs.
- The method combines a node-weighted Laplacian, randomized approximations, and weighted vertex-cover approximations.
- The authors report that existing state-of-the-art methods can be non-near-optimal and sometimes perform worse than random site percolation.
- The approach may support cost-effective immunization and disruption strategies in social and transportation networks, as well as more robust system designs.
- The authors restrict legitimate applications to appropriate contexts and warn that dismantling misinformation networks can become censorship or obstruct true information.