I'd like to think that social media doesn't have a significant affect on the nature of my relationships, at least not the important ones. It's a just a communication tool. And in the absence of one tool, I'd pick up another. I think this is true for my deepest, most important relationships.
I don't talk a lot with my parents who live 2,000 miles away, but when I do, it's usually over the phone or when they come to visit. If I used Facebook to talk with them, would it change the nature of our relationship? No. It wouldn't. The same goes for my closest friends. Social media doesn't factor into how or if I relate to my friends, it's simply a medium to communicate with them. And if I didn't have this medium, I'd use a different one. Maybe we'd communicate less frequently, but it wouldn't change the nature of our relationship.
The exception is lower-level relationships – my high school friends, the people I took a class with, or worked with at a previous job. I could be persuaded to believe that the nature of these relationships might be altered by the availability of a quick and consistent method of communicating. For this class of relationship, without social media, there would be no relationship. I would not pick up an alternative tool to communicate with them. We would just stop talking, and the relationship would disappear into the past.
There's no doubt that social media has changed the way we communicate. But human beings are by nature, a social animal. We've always been relational. And in my view (ever-evolving), the presence of new communication tools does not alter the nature of our relationships to one another.