What the meaning of "vertices induce hyperedges" in hypergraphs?

Question

I don't understand what's the meaning of the word "induce" regrading hypergraphs. For example, "3 vertices induce 2 hyperedges".

I would be glad if you could draw it and explain the meaning of the word.

Edit: I saw the term in the following article, page 2, the second point of Conjecture 1: https://www.dropbox.com/s/w39zlg08piiwi9d/DominationIn3Tournaments.pdf?dl=0

The domination number of a 3-tournament such that any four of its vertices induce at least two edges with the same tail is bounded by a constant.

Answer 1

Vertices in hypergraphs induce hyperedges in the same way that vertices in graphs induce edges.

That is, an induced subgraph of a (hyper)graph $G$ is a subgraph that includes an edge $e$ of $G$ whenever all vertices of $e$ are included. In particular, the subgraph $G[S]$ induced by a vertex set $S$ is the unique induced subgraph which has vertex set $S$: its edges are all the edges of $G$ contained in $S$.

A slightly-informal phrase such as

any four of its vertices induce at least two edges with the same tail

that doesn't talk about induced subgraphs directly is meant to unpack to something like

any set of four vertices induces a subgraph that contains two edges with the same tail.