A tournament is a directed graph

Directed graph

A directed graph or digraph is a pair G= of:* a set V, whose elements are called vertices or nodes,...

 (digraph) obtained by assigning a direction for each edge in an undirected complete graph

Complete graph

In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge.-Properties:...

. That is, it is a directed graph in which every pair of vertices is connected by a single directed edge.

Many of the important properties of tournaments were first investigated by Landau in order to model dominance relations in flocks of chickens. Current applications of tournaments include the study of voting theory and social choice theory

Social choice theory

Social choice theory is a theoretical framework for measuring individual interests, values, or welfares as an aggregate towards collective decision. A non-theoretical example of a collective decision is passing a set of laws under a constitution. Social choice theory dates from Condorcet's...

 among other things.