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complete graph

simple undirected graph in which every pair of distinct vertices is connected by a unique edge
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complete graph

Summary

complete graph is a hereditary graph class[1]. It has Wikipedia articles in 24 language editions, a strong signal of global cultural recognition.[2]

Key Facts

  • complete graph's instance of is recorded as hereditary graph class[3].
  • complete graph is a type of undirected graph[4].
  • complete graph is a type of connected graph[5].
  • complete graph is a type of cluster graph[6].
  • complete graph is a type of block graph[7].
  • complete graph is a type of balanced complete multipartite graph[8].
  • complete graph is a type of threshold graph[9].
  • complete graph is a type of Hamming graph[10].
  • complete graph is a type of Kneser graph[11].
  • complete graph is a type of traceable graph[12].
  • complete graph is a type of Hamilton-connected graph[13].
  • complete graph is a type of symmetric graph[14].
  • complete graph is a type of strongly regular graph[15].
  • complete graph is a type of uniquely colorable graph[16].
  • complete graph is a type of integral graph[17].
  • complete graph is a type of geodetic graph[18].
  • complete graph is a type of circulant graph[19].
  • complete graph is a type of gridline graph[20].
  • complete graph is a type of dense graph[21].
  • complete graph is a type of Turán graph[22].
  • complete graph is a type of core[23].
  • complete graph is a type of Sierpiński graph[24].
  • complete graph is a type of polytopal graph[25].
  • complete graph is a type of rook's graph[26].
  • complete graph is a type of queen's graph[27].

Body

Definition and Type

complete graph's instance of is recorded as hereditary graph class[3]. Recorded subclass of include undirected graph[4], connected graph[5], cluster graph[6], block graph[7], balanced complete multipartite graph[8], and threshold graph[9]. It is the opposite of edgeless graph[28].

Why It Matters

complete graph has Wikipedia articles in 24 language editions, a strong signal of global cultural recognition.[2] It is known by 18 alternative names across languages and contexts.[29]

Related Entities

graph theory

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] ↑ . wikidata.org.
  2. [4] ↑ . wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . wikidata.org.
  6. [8] ↑ . wikidata.org.
  7. [9] ↑ . wikidata.org.
  8. [10] ↑ . wikidata.org.
  9. [11] ↑ . wikidata.org.
  10. [12] ↑ . wikidata.org.
  11. [13] ↑ . wikidata.org.
  12. [14] ↑ . wikidata.org.
  13. [15] ↑ . wikidata.org.
  14. [16] ↑ . wikidata.org.
  15. [17] ↑ . wikidata.org.
  16. [18] ↑ . wikidata.org.
  17. [19] ↑ . wikidata.org.
  18. [20] ↑ . wikidata.org.
  19. [21] ↑ . wikidata.org.
  20. [22] ↑ . wikidata.org.
  21. [23] ↑ . wikidata.org.
  22. [24] ↑ . wikidata.org.
  23. [25] ↑ . wikidata.org.
  24. [26] ↑ . wikidata.org.
  25. [27] ↑ . wikidata.org.
  26. [28] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikidata sitelinks. wikidata.org.
  2. [29] ↑ . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). complete graph. Retrieved May 3, 2026, from https://4ort.xyz/entity/complete-graph
MLA “complete graph.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/complete-graph.
BibTeX @misc{4ortxyz_complete-graph_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{complete graph}}, year = {2026}, url = {https://4ort.xyz/entity/complete-graph}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): complete graph — https://4ort.xyz/entity/complete-graph (retrieved 2026-05-03)

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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 2d ago · Mynus grey · 2026-07-02 view diff on Wikidata ↗
    P14534 → SimpleGraph.completeGraph
    "/* wbcreateclaim-create:1| */ [[Property:P14534]]: SimpleGraph.completeGraph, #quickstatements; #temporary_batch_1783013068346"
  2. 6w ago · Twofivesixbot bot · 2026-05-23 view diff on Wikidata ↗
    Subclass of → —
    Graph diameter → {'amount': '+1'}
    Instance of → —
    Has characteristic → vertex connectivity, edge-connectivity
    + 8 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-update-qualifiers:1||1|3 */ [[Property:P8189]]: 987007545781605171, mv to monolingual text names on J9U statements"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.