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Construction junctions are diamonds. They show where multiple structures must coexist on the same carrier and satisfy compatibility conditions.

Canonical static concept record

Complete graph

Open this concept in the interactive graph Read the Markdown equivalent

Summary

A simple graph in which every pair of distinct vertices is adjacent.

Record metadata

Canonical name: Complete graph
Concept ID: complete_graph
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Combinatorics & graph theory
Domains: Combinatorics & graph theory
Alternate terminology: No alternate terminology is currently authored for this record.

Carrier(s)

vertex set $V$

Data

all two-element subsets of $V$ as edges

Axioms / constraints

each pair of distinct vertices is joined by exactly one edge

Canonically induces

maximal edge set among simple graphs on $V$

Notes

The complete graph on $n$ vertices is denoted $K_n$ .

Concept sources

Wikipedia — Complete graph — Complete graph · encyclopedic reference · source ID wp-complete-graph
nLab — complete graph — complete graph · mathematical reference · source ID nlab-complete-graph
Diestel — Graph Theory — Graph Theory · textbook · source ID diestel-graph-theory

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Simple graph Complete graph

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: simple_graph_to_complete_graph
Relation type: Impose axiom impose-axiom
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: + every possible edge

Authored explanation

Require every pair of distinct vertices to be adjacent.

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Wikipedia — Complete graph — Complete graph · encyclopedic reference · source ID wp-complete-graph
nLab — complete graph — complete graph · mathematical reference · source ID nlab-complete-graph
Diestel — Graph Theory — Graph Theory · textbook · source ID diestel-graph-theory

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

No direct relations are authored in this direction.

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