An alpha group is a set of vertices in which each vertex is connected to every other vertex. Figure 6.15 shows an alpha group of size 4. (a) Suppose we are looking for pairs of vertices that share at...

An alpha group is a set of vertices in which each vertex is connected to every other vertex. Figure 6.15 shows an alpha group of size 4.

(a) Suppose we are looking for pairs of vertices that share at least two neighboring nodes. How many pairs of vertices would we get for an alpha group of size 4? How many in alpha group of size 5? Size 6?

(b) Using your results from part (a), devise a function that finds how many pairs of vertices have at least two common neighbors in an alpha group of size n. (Hint: also think about alpha groups of size 3 or less.)

Figure 6.15