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Mathematical Object

Complete Graph

Combinatorics and Graph Theory

In graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge; a complete digraph is the directed analogue, in which every pair of distinct vertices is connected by a pair of unique edges, one in each direction. Graph theory itself is typically dated to Leonhard Euler's 1736 work on the Seven Bridges of Konigsberg, but drawings of complete graphs, with vertices placed on the points of a regular polygon, had already appeared in the thirteenth century in the work of Ramon Llull, where such a drawing is sometimes called a mystic rose.

Facts
Classification
Object Kind
Geometric Object 1
Connections

In Branch

Source Wikipedia: Complete graph

Is Kind Of Object

Entity-backed identity for the object-kind enum value this mathematical object already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The object-kind fact itself stays on the object unchanged.

Sources
1. Wikipedia: Complete graph
  • Lead section, first sentence
    a simple undirected graph in which every pair of distinct vertices is connected by a unique edge
  • In Branch: Graph Theory, Lead sentence
    In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices
View the Source
Complete Graph, from Wolfram MathWorld
Definition, first paragraph
Quote, Definition, first paragraph
A complete graph is a graph in which each pair of graph vertices is connected by an edge.
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