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This paper addresses these challenges using\n            <jats:italic toggle=\"yes\">local differential privacy (LDP)<\/jats:italic>\n            , which enforces privacy at the individual level, where\n            <jats:italic toggle=\"yes\">no third-party entity is trusted<\/jats:italic>\n            , unlike centralized models that assume a trusted curator.\n          <\/jats:p>\n          <jats:p>\n            We introduce novel LDP algorithms for two fundamental graph statistics:\n            <jats:italic toggle=\"yes\">k<\/jats:italic>\n            -core decomposition and triangle counting. Our approach leverages input-dependent private graph properties\u2014specifically degeneracy and maximum degree\u2014to improve theoretical utility. Unlike prior methods, our error bounds depend on the maximum degree rather than the total edge count, yielding significantly tighter guarantees. For triangle counting, we improve on the work of Imola, Murakami, and Chaudhury [USENIX Security '21, '22], which bounds error in terms of edge count. Our algorithm instead achieves bounds based on degeneracy by leveraging a private out-degree orientation, a refined variant of Eden et al.'s randomized response technique [ICALP '23], and a novel analysis, yielding stronger guarantees than prior work.\n          <\/jats:p>\n          <jats:p>\n            Beyond theoretical gains, we are the first to evaluate local DP algorithms in a distributed simulation, unlike prior work tested on a single processor. Experiments on real-world graphs show substantial accuracy gains: our\n            <jats:italic toggle=\"yes\">k<\/jats:italic>\n            -core decomposition achieves errors within 3\n            <jats:bold>x<\/jats:bold>\n            of exact values, far outperforming the 131x error in the baseline of Dhulipala et al. [FOCS '22]. Our triangle counting algorithm reduces multiplicative approximation errors by up to\n            <jats:bold>six orders of magnitude<\/jats:bold>\n            , while maintaining competitive runtime.\n          <\/jats:p>","DOI":"10.14778\/3749646.3749687","type":"journal-article","created":{"date-parts":[[2025,9,4]],"date-time":"2025-09-04T17:55:06Z","timestamp":1757008506000},"page":"4199-4213","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Practical and Accurate Local Edge Differentially Private Graph Algorithms"],"prefix":"10.14778","volume":"18","author":[{"given":"Pranay","family":"Mundra","sequence":"first","affiliation":[{"name":"Yale University, New Haven, CT, USA"}]},{"given":"Charalampos","family":"Papamanthou","sequence":"additional","affiliation":[{"name":"Yale University, New Haven, CT, USA"}]},{"given":"Julian","family":"Shun","sequence":"additional","affiliation":[{"name":"MIT CSAIL, Cambridge, MA, USA"}]},{"given":"Quanquan C.","family":"Liu","sequence":"additional","affiliation":[{"name":"Yale University, New Haven, CT, USA"}]}],"member":"320","published-online":{"date-parts":[[2025,9,4]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"2024. 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