turan_graph

turan_graph(n, r)

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.