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After a brief introduction and the establishment of notation and terminology, we catalogue characterizations proposed in journal articles published within the last two decades. We then describe some of the numerous application areas for such characterizations. We experiment with implementations of numerous characteristics on several graph-generation models, after which we conclude with a discussion of open problems and future directions.<\/jats:p>","DOI":"10.1093\/comnet\/cnab018","type":"journal-article","created":{"date-parts":[[2021,4,28]],"date-time":"2021-04-28T19:55:00Z","timestamp":1619639700000},"source":"Crossref","is-referenced-by-count":10,"title":["Characterization of robustness and resilience in graphs: a mini-review"],"prefix":"10.1093","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6300-7208","authenticated-orcid":false,"given":"S E","family":"Schaeffer","sequence":"first","affiliation":[{"name":"Facultad de Ingenier\u00eda Mec\u00e1nica y El\u00e9ctrica, Universidad Aut\u00f3noma de Nuevo Le\u00f3n, San Nicol\u00e1s de los Garza, Nuevo Le\u00f3n, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V","family":"Vald\u00e9s","sequence":"additional","affiliation":[{"name":"NIC Chile Research Labs, Universidad de Chile, Nuevo Le\u00f3n, Santiago, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J","family":"Figols","sequence":"additional","affiliation":[{"name":"NIC Chile Research Labs, Universidad de Chile, Nuevo Le\u00f3n, Santiago, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I","family":"Bachmann","sequence":"additional","affiliation":[{"name":"NIC Chile Research Labs, Universidad de Chile, Nuevo Le\u00f3n, Santiago, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F","family":"Morales","sequence":"additional","affiliation":[{"name":"NIC Chile Research Labs, Universidad de Chile, Nuevo Le\u00f3n, Santiago, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0036-2004","authenticated-orcid":false,"given":"J","family":"Bustos-Jim\u00e9nez","sequence":"additional","affiliation":[{"name":"NIC Chile Research Labs, Universidad de Chile, Nuevo Le\u00f3n, Santiago, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2021,5,27]]},"reference":[{"key":"2021080511131974600_B1","doi-asserted-by":"crossref","first-page":"4626","DOI":"10.1103\/PhysRevLett.85.4626","article-title":"Resilience of the internet to random breakdowns","volume":"85","author":"Cohen,","year":"2000","journal-title":"Phys. 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