{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T21:57:23Z","timestamp":1781647043512,"version":"3.54.5"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T00:00:00Z","timestamp":1775347200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T00:00:00Z","timestamp":1779148800000},"content-version":"vor","delay-in-days":44,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"crossref","award":["ANR-16-CONV-0004"],"award-info":[{"award-number":["ANR-16-CONV-0004"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Central African Forest Initiative"},{"DOI":"10.13039\/501100011061","name":"Agence Fran\u00e7aise de D\u00e9veloppement","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100011061","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Netw Sci"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The response of a network to connectivity disruption is central to understanding its robustness. While such questions have been thoroughly studied in terms of global cohesion, many questions remain open regarding the impact on local connectivity. Specifically, networks with different topologies display different distributions of small motifs, and it remains unclear how local connectivity patterns link to structural weaknesses within a network. This study presents a principled approach for assessing random connectivity disruptions among the nodes of a network to identify its structural vulnerabilities. Leveraging recent findings on random walks for exact local topology recollection, we introduce a method for quantifying changes within the (l)-hop neighborhood of the nodes. We derive vulnerability profiles for the nodes and introduce a new index that aggregates neighboring nodes\u2019 vulnerabilities in a distance dependent weighting. Our conducted experiments show that structural weaknesses of a network are distributed across localized regions, where vulnerabilities are most likely driven by immediate neighborhoods of the nodes.<\/jats:p>","DOI":"10.1007\/s41109-026-00788-1","type":"journal-article","created":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T15:44:41Z","timestamp":1775403881000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["From random perturbations to localized vulnerabilities"],"prefix":"10.1007","volume":"11","author":[{"given":"Anas","family":"Zakroum","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roberto","family":"Interdonato","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pascal","family":"Degenne","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mathieu","family":"Roche","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Danny Lo","family":"Seen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,5]]},"reference":[{"issue":"6794","key":"788_CR1","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1038\/35019019","volume":"406","author":"R Albert","year":"2000","unstructured":"Albert R, Jeong H, Barab\u00e1si A-L (2000) Error and attack tolerance of complex networks. Nature 406(6794):378\u2013382","journal-title":"Nature"},{"issue":"10","key":"788_CR2","doi-asserted-by":"publisher","first-page":"943","DOI":"10.1002\/ps.1347","volume":"63","author":"P Andras","year":"2007","unstructured":"Andras P, Gwyther R, Madalinski AA, Lynden SJ, Andras A, Young MP (2007) Ecological network analysis: an application to the evaluation of effects of pesticide use in an agricultural environment. Pest Manag Sci Form Pesticide Sci 63(10):943\u2013953","journal-title":"Pest Manag Sci Form Pesticide Sci"},{"issue":"2","key":"788_CR3","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1038\/s42254-023-00676-y","volume":"6","author":"O Artime","year":"2024","unstructured":"Artime O, Grassia M, De Domenico M, Gleeson JP, Makse HA, Mangioni G, Perc M, Radicchi F (2024) Robustness and resilience of complex networks. Nat Rev Phys 6(2):114\u2013131","journal-title":"Nat Rev Phys"},{"issue":"2","key":"788_CR4","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/S0967-070X(02)00011-2","volume":"9","author":"K Berdica","year":"2002","unstructured":"Berdica K (2002) An introduction to road vulnerability: what has been done, is done and should be done. Transp Policy 9(2):117\u2013127","journal-title":"Transp Policy"},{"issue":"4","key":"788_CR5","doi-asserted-by":"publisher","first-page":"985","DOI":"10.1063\/1.1505810","volume":"12","author":"BA Carreras","year":"2002","unstructured":"Carreras BA, Lynch VE, Dobson I, Newman DE (2002) Critical points and transitions in an electric power transmission model for cascading failure blackouts. Chaos Interdiscip J Nonlinear Sci 12(4):985\u2013994","journal-title":"Chaos Interdiscip J Nonlinear Sci"},{"key":"788_CR6","doi-asserted-by":"publisher","first-page":"1395","DOI":"10.1007\/s10618-015-0447-5","volume":"30","author":"H Chan","year":"2016","unstructured":"Chan H, Akoglu L (2016) Optimizing network robustness by edge rewiring: a general framework. Data Min Knowl Disc 30:1395\u20131425","journal-title":"Data Min Knowl Disc"},{"key":"788_CR7","doi-asserted-by":"crossref","unstructured":"Chan H, Akoglu L, Tong H (2014) Make it or break it: manipulating robustness in large networks. In: Proceedings of the 2014 SIAM international conference on data mining, SIAM, pp 325\u2013333","DOI":"10.1137\/1.9781611973440.37"},{"key":"788_CR8","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.softx.2016.05.002","volume":"5","author":"P Degenne","year":"2016","unstructured":"Degenne P, Lo Seen D (2016) Ocelet: simulating processes of landscape changes using interaction graphs. SoftwareX 5:89\u201395","journal-title":"SoftwareX"},{"key":"788_CR9","unstructured":"Ellens W, Kooij RE (2013) Graph measures and network robustness. arXiv preprint arXiv:1311.5064"},{"issue":"10","key":"788_CR10","doi-asserted-by":"publisher","first-page":"2491","DOI":"10.1016\/j.laa.2011.02.024","volume":"435","author":"W Ellens","year":"2011","unstructured":"Ellens W, Spieksma FM, Van Mieghem P, Jamakovic A, Kooij RE (2011) Effective graph resistance. Linear Algebra Appl 435(10):2491\u20132506","journal-title":"Linear Algebra Appl"},{"issue":"6","key":"788_CR11","first-page":"5915","volume":"35","author":"S Freitas","year":"2022","unstructured":"Freitas S, Yang D, Kumar S, Tong H, Chau DH (2022) Graph vulnerability and robustness: a survey. IEEE Trans Knowl Data Eng 35(6):5915\u20135934","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"4","key":"788_CR12","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1111\/j.1539-6924.2006.00791.x","volume":"26","author":"\u00c5J Holmgren","year":"2006","unstructured":"Holmgren \u00c5J (2006) Using graph models to analyze the vulnerability of electric power networks. Risk Anal 26(4):955\u2013969","journal-title":"Risk Anal"},{"key":"788_CR13","unstructured":"Ivanov S, Burnaev E (2018) Anonymous walk embeddings. In: International conference on machine learning, PMLR, pp 2186\u20132195"},{"key":"788_CR14","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.dam.2015.06.035","volume":"200","author":"S Micali","year":"2016","unstructured":"Micali S, Zhu ZA (2016) Reconstructing markov processes from independent and anonymous experiments. Discret Appl Math 200:108\u2013122","journal-title":"Discret Appl Math"},{"issue":"7563","key":"788_CR15","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1038\/nature14604","volume":"524","author":"F Morone","year":"2015","unstructured":"Morone F, Makse HA (2015) Influence maximization in complex networks through optimal percolation. Nature 524(7563):65\u201368","journal-title":"Nature"},{"key":"788_CR16","doi-asserted-by":"publisher","first-page":"30062","DOI":"10.1038\/srep30062","volume":"6","author":"F Morone","year":"2016","unstructured":"Morone F, Min B, Bo L, Mari R, Makse HA (2016) Collective influence algorithm to find influencers via optimal percolation in massively large social media. Sci Rep 6:30062. https:\/\/doi.org\/10.1038\/srep30062. arXiv:1603.08273 [physics.soc-ph]","journal-title":"Sci Rep"},{"issue":"6","key":"788_CR17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.66.065102","volume":"66","author":"AE Motter","year":"2002","unstructured":"Motter AE, Lai Y-C (2002) Cascade-based attacks on complex networks. Phys Rev E 66(6):065102","journal-title":"Phys Rev E"},{"issue":"1","key":"788_CR18","doi-asserted-by":"publisher","first-page":"3599","DOI":"10.1038\/s41598-020-60501-9","volume":"10","author":"G Moutsinas","year":"2020","unstructured":"Moutsinas G, Guo W (2020) Node-level resilience loss in dynamic complex networks. Sci Rep 10(1):3599","journal-title":"Sci Rep"},{"issue":"14","key":"788_CR19","doi-asserted-by":"publisher","first-page":"6554","DOI":"10.1073\/pnas.1806108116","volume":"116","author":"X-L Ren","year":"2019","unstructured":"Ren X-L, Gleinig N, Helbing D, Antulov-Fantulin N (2019) Generalized network dismantling. Proc Natl Acad Sci 116(14):6554\u20136559","journal-title":"Proc Natl Acad Sci"},{"issue":"10","key":"788_CR20","doi-asserted-by":"publisher","first-page":"3838","DOI":"10.1073\/pnas.1009440108","volume":"108","author":"CM Schneider","year":"2011","unstructured":"Schneider CM, Moreira AA, Andrade JS Jr, Havlin S, Herrmann HJ (2011) Mitigation of malicious attacks on networks. Proc Natl Acad Sci 108(10):3838\u20133841","journal-title":"Proc Natl Acad Sci"},{"key":"788_CR21","first-page":"8924087","volume":"1","author":"KK Shah","year":"2021","unstructured":"Shah KK, Modi B, Pandey HP, Subedi A, Aryal G, Pandey M, Shrestha J (2021) Diversified crop rotation: an approach for sustainable agriculture production. Adv Agric 1:8924087","journal-title":"Adv Agric"},{"issue":"3","key":"788_CR22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.032303","volume":"100","author":"M Tyloo","year":"2019","unstructured":"Tyloo M, Jacquod P (2019) Global robustness versus local vulnerabilities in complex synchronous networks. Phys Rev E 100(3):032303","journal-title":"Phys Rev E"},{"issue":"4","key":"788_CR23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.105.044126","volume":"105","author":"A Valente","year":"2022","unstructured":"Valente A, De Domenico M, Artime O (2022) Non-Markovian random walks characterize network robustness to nonlocal cascades. Phys Rev E 105(4):044126","journal-title":"Phys Rev E"},{"issue":"1","key":"788_CR24","doi-asserted-by":"publisher","first-page":"13513","DOI":"10.1038\/s41598-018-31902-8","volume":"8","author":"S Wandelt","year":"2018","unstructured":"Wandelt S, Sun X, Feng D, Zanin M, Havlin S (2018) A comparative analysis of approaches to network-dismantling. Sci Rep 8(1):13513","journal-title":"Sci Rep"},{"key":"788_CR25","doi-asserted-by":"crossref","unstructured":"Yan Y, Hu Y, Zhou Q, Wu S, Wang D, Tong H (2024) Topological anonymous walk embedding: a new structural node embedding approach. In: Proceedings of the 33rd ACM international conference on information and knowledge management, pp 2796\u20132806","DOI":"10.1145\/3627673.3679565"},{"key":"788_CR26","doi-asserted-by":"crossref","unstructured":"Zeng Y, Huang Y, Ren X-L, L\u00fc L (2024) Identifying vital nodes through augmented random walks on higher-order networks. Inf Sci 121067","DOI":"10.1016\/j.ins.2024.121067"}],"container-title":["Applied Network Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s41109-026-00788-1","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41109-026-00788-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41109-026-00788-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T21:29:46Z","timestamp":1781645386000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s41109-026-00788-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,5]]},"references-count":26,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["788"],"URL":"https:\/\/doi.org\/10.1007\/s41109-026-00788-1","relation":{},"ISSN":["2364-8228"],"issn-type":[{"value":"2364-8228","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,5]]},"assertion":[{"value":"1 July 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 February 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 April 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare no conflict of interest.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"39"}}