Term for a fully connected balanced graph (Rock paper scissor)

Question

Is there a mathematical, graph theory, game theory term for a graph that is fully connected and balanced evenly with each other node.

I'm thinking in situations like Rock paper scissors where each action is equally balanced by each other option?

Answer 1

A regular tournament $T=(V,E)$ is a complete digraph on $|V|=2n+1$ vertices where each vertex has the same score as each other vertex. Each vertex is connected to each other vertex by exactly one directed edge and each vertex dominates exactly $\frac{|V|-1}{2}$ other edges and is dominated by the $\frac{|V|-1}{2}$ other edges.