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In many anonymous networks, such as blockchain cryptocurrencies, dark web message boards, and other illicit networks, nodes are anonymous to outsiders, however the existence of a link between individuals is observable. For example, in blockchains, transactions between anonymous accounts are published openly. Here we consider what happens if one or more individuals in such a network are deanonymized by an outside investigator. These compromised individuals could then potentially leak information about others with whom they interacted, leading to a cascade of nodes\u2019 identities being revealed. We map this scenario to percolation and analyze its consequences on three real anonymous networks\u2014(1) a blockchain transaction network, (2) interactions on the dark web, and (3) a political conspiracy network. We quantify, for different likelihoods of individuals possessing information on their neighbors, <jats:italic>p<\/jats:italic>, the fraction of accounts that can be identified in each network. We then estimate the minimum and most probable number of steps to a desired anonymous node, a measure of the effort to deanonymize that node. In all three networks, we find that it is possible to deanonymize a significant fraction of the network (<jats:inline-formula><jats:alternatives><jats:tex-math>$&gt;50\\%$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mo>&gt;<\/mml:mo>\n                  <mml:mn>50<\/mml:mn>\n                  <mml:mi>%<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>) within less than 5 steps for values of <jats:inline-formula><jats:alternatives><jats:tex-math>$p&gt;0.4$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>p<\/mml:mi>\n                  <mml:mo>&gt;<\/mml:mo>\n                  <mml:mn>0.4<\/mml:mn>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. We show how existing measures and approaches from percolation theory can help investigators quantify the chances of deanonymizing individuals, as well as how users can maintain privacy.<\/jats:p>","DOI":"10.1140\/epjds\/s13688-023-00392-8","type":"journal-article","created":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T09:02:33Z","timestamp":1685350953000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Percolation framework reveals limits of privacy in conspiracy, dark web, and blockchain networks"],"prefix":"10.1140","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5273-8363","authenticated-orcid":false,"given":"Louis M.","family":"Shekhtman","sequence":"first","affiliation":[]},{"given":"Alon","family":"Sela","sequence":"additional","affiliation":[]},{"given":"Shlomo","family":"Havlin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,29]]},"reference":[{"key":"392_CR1","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1145\/1526709.1526781","volume-title":"Proceedings of the 18th international conference on world wide web","author":"E Zheleva","year":"2009","unstructured":"Zheleva E, Getoor L (2009) To join or not to join: the illusion of privacy in social networks with mixed public and private user profiles. 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