Many parents don't really "get" this whole social networking thing. Some parents simply don't want to know. Others really want to know so they can understand what their kids are doing online.
One of the challenges that some adults find in social networks is that they aren't comfortable with the netiquette on a given site. They are perfectly functional adults in every other social situation, but when they get online, the rules are different. Until someone tells them the etiquette, they don't know what "normal" is. If they want to sign up for a profile on one or more of the same sites as their kid, they will most likely want to link to your, i.e. their child's, profile.
Here are some things to keep in mind when introducing parents to the world of social networking:
-- Have them ask you before they ask to "friend" any of your friends. It doesn't mean they have to, or will, but can't hurt to ask if you think they might embarrass you.
-- Explain how linking to different profiles works (you can opt to accept or decline an invitation to be linked to someone else's profile, etc.)
-- Ask your parent how they are going to use the site and show them how to do what they want to do. Are they going to email, post pictures, send virtual gifts, send IM's, seek out others with their interests, etc?
-- Teach them how the privacy settings work. This is to avoid having them post that embarrassing 1st grade picture of you with no front teeth for the world to see.
If they sign up for a network different than yours, your parents will probably still appreciate the help. It is a great opportunity to show how savvy you have become!
Do you (or would you) let your parents be your "friend" on your social networking site?