CompleteGraph¶

CompleteGraph[n] is the complete graph on n vertices — every pair of vertices is connected, giving n (n-1)/2 edges.

$ wo 'EdgeCount[CompleteGraph[4]]'
6

CompleteGraph[{n1, n2, ...}] is the complete multipartite graph: vertices are split into groups of the given sizes and joined only across different groups.

$ wo 'EdgeCount[CompleteGraph[{2, 3}]]'
6

$ wo 'VertexCount[CompleteGraph[{2, 3}]]'
5

Such a graph is bipartite.

$ wo 'BipartiteGraphQ[CompleteGraph[{2, 3}]]'
True