Complete Graph

Topics: Graph Theory - Graph

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(definition)

A complete graph is a simple graph such that every pair of vertices is joined by an edge. As such, we can say that every pair of vertices is adjacent.

We denote a complete graph with $K_n$, where $n$ is the number of vertices.

Number of Lines

A $K_n$ graph has exactly $\frac{n(n-1)}{2}$ edges.

Simplices

Notice that every $n$-simplex is a $K_{n+1}$ complete graph.