IsTournament returns true if the input graph is a tournament. It returns false otherwise.

A tournament is a directed graph G that satisfies the following property: for every pair of vertices u and v in G exactly one of the directed edges $\left[u\,v\right]$ or $\left[v\,u\right]$ is in G.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{T1}≔\mathrm{Digraph}\left(\left\{\left[1\,2\right]\,\left[2\,3\right]\,\left[3\,1\right]\right\}\right)$

$\mathrm{T1}≔\mathrm{Graph\; 1:\; a\; directed\; unweighted\; graph\; with\; 3\; vertices\; and\; 3\; arc(s)}$

$\mathrm{IsTournament}\left(\mathrm{T1}\right)$

$\mathrm{true}$

$\mathrm{T2}≔\mathrm{Digraph}\left(\left\{\left[1\,2\right]\,\left[1\,3\right]\,\left[2\,3\right]\,\left[3\,1\right]\right\}\right)$

$\mathrm{T2}≔\mathrm{Graph\; 2:\; a\; directed\; unweighted\; graph\; with\; 3\; vertices\; and\; 4\; arc(s)}$

$\mathrm{IsTournament}\left(\mathrm{T2}\right)$

$\mathrm{false}$

$\mathrm{T3}≔\mathrm{Digraph}\left(\left\{\left[1\,2\right]\,\left[2\,3\right]\right\}\right)$

$\mathrm{T3}≔\mathrm{Graph\; 3:\; a\; directed\; unweighted\; graph\; with\; 3\; vertices\; and\; 2\; arc(s)}$

$\mathrm{IsTournament}\left(\mathrm{T3}\right)$

$\mathrm{false}$