JMO 1997 Problem 3

Call the Graph the set which composed of several vertices $P_1,\ \cdots P_2$ and several edges $($ s egment s $)$ connecting two points among these vertices. Now let $G$ be a graph with 9 vertices and satisfies the following condition.

Condition: Even if we select any five points from the vertices in $G,$ there exist at least two edges whose endpoints are included in the set of 5 points.

What is the minimum possible numbers of edges satisfying the condition?