{"id":6080,"date":"2025-08-14T07:02:53","date_gmt":"2025-08-14T07:02:53","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/08\/14\/2508-09412\/"},"modified":"2025-08-14T07:02:53","modified_gmt":"2025-08-14T07:02:53","slug":"2508-09412","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/08\/14\/2508-09412\/","title":{"rendered":"A pseudo-inverse of a line graph"},"content":{"rendered":"<p>    A pseudo-inverse of a line graph<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2508.09412v1 Announce Type: new<br \/>\nAbstract: Line graphs are an alternative representation of graphs where each vertex of the original (root) graph becomes an edge. However not all graphs have a corresponding root graph, hence the transformation from graphs to line graphs is not invertible. We investigate the case when there is a small perturbation in the space of line graphs, and try to recover the corresponding root graph, essentially defining the inverse of the line graph operation. We propose a linear integer program that edits the smallest number of edges in the line graph, that allow a root graph to be found. We use the spectral norm to theoretically prove that such a pseudo-inverse operation is well behaved. Illustrative empirical experiments on ErdH{o}s-R&#8217;enyi graphs show that our theoretical results work in practice.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Sevvandi Kandanaarachchi, Philip Kilby, Cheng Soon Ong<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2508.09412\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A pseudo-inverse of a line graph arXiv:2508.09412v1 Announce Type: new Abstract: Line graphs are an alternative representation of graphs where each vertex of the original (root) graph becomes an edge. However not all graphs have a corresponding root graph, hence the transformation from graphs to line graphs is not invertible. We investigate the case when [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,376,112],"tags":[339,2555,2022],"class_list":["post-6080","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-oc","category-stat-ml","tag-graph","tag-graphs","tag-line"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/6080"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=6080"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/6080\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=6080"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=6080"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=6080"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}