{"id":"graph-theory","domain":"discrete","type":"Concept","title":"Graph Theory","slug":"graph-theory","url":"/mathematics/discrete/graph-theory/","summary":"Studies networks of vertices connected by edges. Founded by Euler's 1736 solution to the Königsberg Bridge Problem. Essential to computer science, biology, logistics, social networks.","founding_problem":"Königsberg Bridge Problem, Euler, 1736","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"West, D.B. (2001). Introduction to Graph Theory. 2nd ed. Prentice Hall."},{"tier":1,"citation":"Euler, L. (1736). Solutio problematis ad geometriam situs pertinentis. Commentarii academiae scientiarum Petropolitanae, 8, 128-140."},{"tier":2,"citation":"Barabási, A-L. and Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509-512."},{"tier":3,"citation":"Hopkins, B. and Wilson, R.J. (2004). The truth about Königsberg. College Mathematics Journal, 35(3), 198-207."}],"relationships":[{"type":"applied_in","target":"four-colour-theorem","label":"Four Colour Theorem"},{"type":"related_to","target":null,"label":"P vs NP — Travelling Salesman Problem"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.5"}