{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.cycle","code":"thing-q245595","url":"https://ver.cy/models/thing/q245595/","name":"cycle","alternateNames":["self-avoiding polygon","induced cycle"],"kind":"thing","status":"published","version":"0.2.0-wave.4","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.TME"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"In graph theory, a cycle is a closed path in a graph that starts and ends at the same vertex, following edges without repeating a vertex in between; the registry aliases name related notions such as an induced cycle and a self-avoiding polygon. Cycles are a basic structure in the study of graphs and networks, and a graph with no cycles is acyclic. This is the mathematical sense, distinct from everyday cycles such as a repeating process.","purpose":"Let an agent explain the graph-theory cycle, relay its definition, kinds and role from mathematics sources, describe the related notions its aliases name, and distinguish it from a path and from everyday senses of cycle.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Closed path","Returns to start","No repeated inner vertex","Basic graph structure"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What a graph cycle is.","layers":[{"id":"definition","name":"Definition","description":"Definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What is a cycle in graph theory, and how does it differ from a path and from an everyday cycle?","kind":"definition"},{"text":"Is the mathematical sense meant?","kind":"boundary"}]}]},{"id":"kinds","name":"Kinds","description":"Kinds.","findings":[{"id":"kinds-finding","name":"Kinds","description":"Kinds.","questions":[{"text":"What are simple, induced and Hamiltonian cycles?","kind":"definition"},{"text":"Which entry fits the specific kind?","kind":"action"}]}]}]},{"id":"theory","name":"Theory","description":"Theory.","layers":[{"id":"role","name":"Role","description":"Role.","findings":[{"id":"role-finding","name":"Role","description":"Role.","questions":[{"text":"Why are cycles important in the study of graphs?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"acyclic","name":"Acyclic","description":"Acyclic graphs.","findings":[{"id":"acyclic-finding","name":"Acyclic","description":"Acyclic.","questions":[{"text":"What does it mean for a graph to be acyclic?","kind":"provenance"},{"text":"Which entry fits acyclic graph?","kind":"action"}]}]}]},{"id":"applications","name":"Applications","description":"Applications.","layers":[{"id":"networks","name":"Networks","description":"Networks.","findings":[{"id":"networks-finding","name":"Networks","description":"Networks.","questions":[{"text":"How do cycles matter in networks and algorithms?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]},{"id":"detection","name":"Detection","description":"Cycle detection.","findings":[{"id":"detection-finding","name":"Detection","description":"Detection.","questions":[{"text":"How are cycles detected in a graph?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]}]},{"id":"context","name":"Context","description":"Context.","layers":[{"id":"graph","name":"Graph","description":"Graphs.","findings":[{"id":"graph-finding","name":"Graph","description":"Graph.","questions":[{"text":"How does a cycle fit the broader idea of a graph?","kind":"provenance"},{"text":"Which entry fits graph?","kind":"action"}]}]},{"id":"senses","name":"Senses","description":"Other senses.","findings":[{"id":"senses-finding","name":"Senses","description":"Senses.","questions":[{"text":"How does the graph cycle differ from cycle as a repeating process?","kind":"provenance"},{"text":"Is the sense correctly identified?","kind":"boundary"}]}]}]}]},"agentConduct":{"may":["Detect and report cycles in graphs, such as dependency graphs, that it is authorized to analyse.","Explain the graph-theory definition and how a cycle differs from an open path or a walk."],"mustNot":["Report a graph as acyclic without checking it completely.","Silently break cycles in someone else's dependency or workflow data by deleting edges.","Mix the graph-theory sense with everyday senses of cycle in technical explanations.","Present a closed walk that repeats vertices as a simple cycle."],"requiresHuman":["Changing a shared dependency structure to remove a cycle that others rely on."]},"ethics":{"considerations":["Undetected cycles can cause deadlocks and endless loops in systems people depend on.","Precise definitions matter for students and for correctness proofs."],"affectedParties":["Students and researchers","Users of affected systems","Software maintainers"]},"owners":{"steward":"Nobody: a mathematical concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q17176291","type":"parent","note":"registry parent class"},{"target":"path","type":"related","note":"related"},{"target":"circuit","type":"related","note":"in registry terms"},{"target":"acyclic graph","type":"related"},{"target":"everyday cycle","type":"related"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.cycle","Wikidata: Q245595 (https://www.wikidata.org/wiki/Q245595)"]},"properties":{"applicability":"not-applicable","items":["field: graph theory note","property: closed, non-repeating path note","registry parent: circuit note"]},"recognition":{"applicability":"optional","items":["A closed path returning to its start in a graph","Induced cycle, self-avoiding polygon","A path does not return to its start; an everyday cycle is a repeating process","Not a physical object; drawn as a loop of vertices joined by edges returning to the start."]},"capabilities":{"applicability":"required","items":["explain the definition","relay kinds and role","describe related notions","distinguish it from a path"]},"hazards":{"applicability":"required","items":["Confusing with an open path","Mixing the math and everyday senses","Conflating cycle kinds"]},"interfaces":{"applicability":"required","items":["Mathematical definition"]},"context":{"applicability":"required","items":["Describing a closed path in a graph.","simple cycle","induced cycle","Hamiltonian cycle"]}},"sources":[{"title":"Wikidata item Q245595: cycle","url":"https://www.wikidata.org/wiki/Q245595","note":"identity and sense of the item"},{"title":"Wikipedia: Cycle (graph theory)","url":"https://en.wikipedia.org/wiki/Cycle_%28graph_theory%29","note":"general description of the item"}],"openQuestions":["Should cycle kinds be separate entries?","How should the everyday sense be signposted?","How should acyclic graphs be linked?"],"resources":{"spec":"/models/things/publications/thing-q245595/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q245595/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-14T03:47:14Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:51:57+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}