Extreme vulnerability to intruder attacks destabilizes network dynamics.

Amirhossein Nazerian, Sahand Tangerami, Malbor Asllani, David Phillips, Hernán Makse, Francesco Sorrentino

Abstract read

In one paragraph

Article in Nature communications, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

0numbers the graph read from it

0cells of the map it votes in

0citing papers in PubMed

–field-weighted citation impact

1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

0 citing papers in PubMed.

No citing paper in PubMed yet.

4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

6 authors.

Amirhossein NazerianDepartment of Mechanical Engineering, University of New Mexico, Albuquerque, NM, USA.ORCID http://orcid.org/0000-0003-1280-2353

Sahand TangeramiDepartment of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran.

Malbor AsllaniDepartment of Mathematics, Florida State University, Tallahassee, USA.ORCID http://orcid.org/0000-0002-3335-429X

David PhillipsDepartment of Mechanical Engineering, University of New Mexico, Albuquerque, NM, USA.

Hernán MakseLevich Institute and Physics Department, City College of New York, New York, NY, USA.ORCID http://orcid.org/0000-0001-6474-1324

Francesco SorrentinoDepartment of Mechanical Engineering, University of New Mexico, Albuquerque, NM, USA. fsorrent@unm.edu.ORCID http://orcid.org/0000-0001-8899-1176

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

Abstract

Consensus, synchronization, formation control, and power grid balance are examples of desirable dynamical states that arise in networks. Here we investigate how such states can be destabilized by an intruder agent within an otherwise functioning network. We see that a single adversarial node, coupled through adversarial connections to one or more other nodes, is sufficient to destabilize the entire network. We further show that concentrating the attack on a single low-indegree node induces the greatest instability, challenging the common assumption that hubs are the most critical nodes. This leads to a new characterization of network vulnerability, identifying low-indegree nodes as the most vulnerable components. Although derived for linear systems, our results extend to nonlinear networks, including the Kuramoto model. These findings reveal an intrinsic vulnerability of technological, social, and biological networks.

Identifiers

PMID42722643

DOI10.1038/s41467-026-76342-5

PMCPMC13562742

What OpenQuestion holds

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Registered trials

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.