# turan_graph#

turan_graph(n, r)[source]#

Return the Turan Graph

The Turan Graph is a complete multipartite graph on $$n$$ nodes with $$r$$ disjoint subsets. That is, edges connect each node to every node not in its subset.

Given $$n$$ and $$r$$, we create a complete multipartite graph with $$r-(n \mod r)$$ partitions of size $$n/r$$, rounded down, and $$n \mod r$$ partitions of size $$n/r+1$$, rounded down.

Parameters:
nint

The number of nodes.

rint

The number of partitions. Must be less than or equal to n.

Notes

Must satisfy $$1 <= r <= n$$. The graph has $$(r-1)(n^2)/(2r)$$ edges, rounded down.