Problem $9(2$ points$)$

Consider the small$-$world phenomenon. Each person knows $30$ people and ranks them from closest to most distant friend. Construct two networks:

$1.$ A "close$-$friend" network: Each person creates an edge to their $10$ closest friends.

$2.$ A "distant$-$friend" network: Each person creates an edge to those friends ranked $21-30.$

Empirical studies show that either $\backslash ($ C $\backslash )($being the set of people reachable in $6$ steps in the close$-$friend network$)$ or $\backslash ($ D $\backslash )($being the set of people reachable in $6$ steps in the distant$-$friend network$)$ is larger.

$($a$)$ Which do you expect the empirical studies show is larger, $\backslash ($ C $\backslash )$ or $\backslash ($ D $\backslash )?$ Explain briefly. $(2$ points$)$