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cycle

vr.tr.cycle · thing-q245595

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.

Thing Registry Cross-cutting context XCT.TME
Bundle → Layer → Finding → QuestionsClassifiersWhat it isWhy it existsDistinguishing featuresWhat robots and AI may and may not doMoral aspectsOwnersLinks to other meta-modelsIdentity and identifiersDirect propertiesRecognitionCapabilities and actionsHazards and failure modesStandards and interfacesContext of useSources

Bundle → Layer → Finding → Questions Filled

4 bundles · 8 layers · 8 findings · 16 questions

Understand What a graph cycle is.

Definition

Definition.

Definition

Definition.

  1. What is a cycle in graph theory, and how does it differ from a path and from an everyday cycle? definition
  2. Is the mathematical sense meant? boundary

Kinds

Kinds.

Kinds

Kinds.

  1. What are simple, induced and Hamiltonian cycles? definition
  2. Which entry fits the specific kind? action
Theory Theory.

Role

Role.

Role

Role.

  1. Why are cycles important in the study of graphs? provenance
  2. Which references are standard? provenance

Acyclic

Acyclic graphs.

Acyclic

Acyclic.

  1. What does it mean for a graph to be acyclic? provenance
  2. Which entry fits acyclic graph? action
Applications Applications.

Networks

Networks.

Networks

Networks.

  1. How do cycles matter in networks and algorithms? provenance
  2. Which sources are cited? provenance

Detection

Cycle detection.

Detection

Detection.

  1. How are cycles detected in a graph? provenance
  2. Which sources are cited? provenance
Context Context.

Graph

Graphs.

Graph

Graph.

  1. How does a cycle fit the broader idea of a graph? provenance
  2. Which entry fits graph? action

Senses

Other senses.

Senses

Senses.

  1. How does the graph cycle differ from cycle as a repeating process? provenance
  2. Is the sense correctly identified? boundary

Classifiers Filled

Family
Thing Registry
Category
Cross-cutting context
Entry kind
thing
Plane
XCT
Domain
XCT.TME
Other names and narrower kinds
self-avoiding polygon, induced cycle

What it is Filled

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.

Why it exists Filled

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.

Distinguishing features Filled

  • Closed path
  • Returns to start
  • No repeated inner vertex
  • Basic graph structure

What robots and AI may and may not do Filled

Must not

  • 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.

Only with a human decision

  • Changing a shared dependency structure to remove a cycle that others rely on.

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.

Moral aspects Filled

  • Undetected cycles can cause deadlocks and endless loops in systems people depend on.
  • Precise definitions matter for students and for correctness proofs.

Who is affected

  • Students and researchers
  • Users of affected systems
  • Software maintainers

Owners Filled

Steward

Nobody: a mathematical concept held in common.

Links to other meta-models Filled

parent

  • Q17176291 - registry parent class

related

  • path - related
  • circuit - in registry terms
  • acyclic graph
  • everyday cycle

What else AI and robots need to interact with it Filled

Identity and identifiers required Filled

  • Vercy registry: vr.tr.cycle
  • Wikidata: Q245595 (https://www.wikidata.org/wiki/Q245595)

Direct properties not applicable Not applicable

  • field: graph theory note
  • property: closed, non-repeating path note
  • registry parent: circuit note

Plane XCT: no invented physical properties.

Recognition optional Filled

  • 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 and actions required Filled

  • explain the definition
  • relay kinds and role
  • describe related notions
  • distinguish it from a path

Hazards and failure modes required Filled

  • Confusing with an open path
  • Mixing the math and everyday senses
  • Conflating cycle kinds

Standards and interfaces required Filled

  • Mathematical definition

Context of use required Filled

  • Describing a closed path in a graph.
  • simple cycle
  • induced cycle
  • Hamiltonian cycle

Sources Filled

  1. Wikidata item Q245595: cycle - identity and sense of the item
  2. Wikipedia: Cycle (graph theory) - general description of the item

Open questions

  • Should cycle kinds be separate entries?
  • How should the everyday sense be signposted?
  • How should acyclic graphs be linked?

Machine files

Card as JSON Specification Card backlog vercy.card/1

Provenance

thing registry research (pass 2) · unreviewed

Built from: models/things/publications/thing-q245595/spec.json