CSolarstorm
New spicy version
Let's say you have two friends. Those two friends each have two other friends, too. Those other four friends each have two friends, too. But those other two friends have no friends except for the previously mentioned ones. That's a dead end to me.
Of course, if you look at it as a circle then I suppose you could say there is no dead end because a circle has neither a begin nor an end, but it isn't a circle, because you are not in contact with those last 8 friends (maybe not even with the four friends of your two friends).
You can only consider it a dead end if you're concerned with everyone having two, exclusive new friends - which isn't necessary. A few of these people will be perfectly happy with two friends, and if they feel unfufilled, they can still make friends with more people up the tree. Not all of them have to be exclusive friends.
Since when is quantity over quality, and more importantly, why is the problem of having more friends valid to school? This is a matter of education, not socially stacking the numbers. I already satisfied your criteria for homeschoolers having friends.