Criticality and universality in network dismantling
Abstract
Identifying the smallest set of elements whose removal dismantle a complex network, known as the network dismantling problem, is a fundamental task with many practical applications. Whereas network dismantling has been extensively studied over the past decade, most work has focused on developing efficient algorithms for large but finite networks. By contrast, the physics of the network dismantling process, namely how the network structural connectivity is affected by the removal of nodes or edges, remains largely unexplored in the thermodynamic limit. Here, we shed light on this understudied aspect of network dismantling by introducing an adaptive biased percolation process able to optimally dismantle a network. Through a systematic analysis of synthetic network models, we find that the proposed percolation process displays a universal phase transition, characterized by the abrupt and simultaneous disappearance of both the giant connected component and the largest 2-core, across networks with markedly different degree distributions. Simulations on real networks further support this universality, indicating that the physics of network dismantling is insensitive to a broad range of topological properties. Together, these results suggest that a topology-agnostic theory could be developed to explain the critical behavior of network dismantling.
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BibTeX
@misc{cirigliano2026criticality,
title = {{Criticality and universality in network dismantling}},
author = {Lorenzo Cirigliano and Claudio Castellano and Minsuk Kim and Filippo Radicchi and Hanlin Sun},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27613},
eprint = {2608.27613},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27613},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Criticality and universality in network dismantling
AU - Lorenzo Cirigliano
AU - Claudio Castellano
AU - Minsuk Kim
AU - Filippo Radicchi
AU - Hanlin Sun
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27613
UR - https://arxiv.org/abs/2608.27613
AB - Identifying the smallest set of elements whose removal dismantle a complex network, known as the network dismantling problem, is a fundamental task with many practical applications. Whereas network dismantling has been extensively studied over the past decade, most work has focused on developing efficient algorithms for large but finite networks. By contrast, the physics of the network dismantling process, namely how the network structural connectivity is affected by the removal of nodes or edges, remains largely unexplored in the thermodynamic limit. Here, we shed light on this understudied aspect of network dismantling by introducing an adaptive biased percolation process able to optimally dismantle a network. Through a systematic analysis of synthetic network models, we find that the proposed percolation process displays a universal phase transition, characterized by the abrupt and simultaneous disappearance of both the giant connected component and the largest 2-core, across networks with markedly different degree distributions. Simulations on real networks further support this universality, indicating that the physics of network dismantling is insensitive to a broad range of topological properties. Together, these results suggest that a topology-agnostic theory could be developed to explain the critical behavior of network dismantling.
ER -