Complete Graph

See: Complete, Graph, Simple Graph, Graph Edge, Graph Node.

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References

2009

• http://en.wikipedia.org/wiki/Complete_graph
  • In the mathematical field of graph theory, a complete graph is a simple graph in which every pair of distinct vertices is connected by an edge. The complete graph on [math]\displaystyle{ n }[/math] vertices has [math]\displaystyle{ n }[/math] vertices and n(n-1)/2 edges, and is denoted by [math]\displaystyle{ K_n }[/math] (from the German komplett). It is a regular graph of degree [math]\displaystyle{ n-1 }[/math]. All complete graphs are their own cliques. They are maximally connected as the only vertex cut which disconnects the graph is the complete set of vertices.
  • A complete graph with [math]\displaystyle{ n }[/math] nodes represents the edges of an (n-1)-simplex. Geometrically [math]\displaystyle{ K_3 }[/math] relates to a triangle, [math]\displaystyle{ K_4 }[/math] a tetrahedron, [math]\displaystyle{ K_5 }[/math] a pentachoron, etc.

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