8. Given 7 points in the plane, what is the minimum number of line segments that need to be connected between them so that any 3 points have a line segment connecting two of them? Try to provide a graph that meets the requirement. (30th IMO Preliminary Question)
8. Let point $A$ among the 7 points have the fewest lines, a total of $k$ lines $A B_{j}, j=1,2, \cdots, k$, and the remaining $6-k$ points are not connected to $A$. Therefore, every two of these $6-k$ points are connected by a line, so the total number of lines in the graph $S \geqslant \frac{1}{2}\{k(k+1)+(6-k)(5-k)\}=k^{2}-5 k+15=\left(k-\frac{5}{2}\right)^{2}+\frac{35}{4} \geqslant\left(\frac{1}{2}\right)^{2}+\frac{35}{4}=9$. On the other hand, as shown in the figure, 9 lines are connected between the 7 points and meet the requirements of the problem, so the minimum number of lines to be connected is 9.