''It would be like a 40-year-old attending the prom or a frat party,'' Rudman says. ''It just doesn't work.''
It's a particular quandary for image-conscious teens, says Eric Kuhn, a junior at Hamilton College in upstate New York, who's blogged about the etiquette of social networking.
He accepted his mom's invitation to be Facebook friends and has, in turn, become online friends with other adults she knows. But so far, he says, his 16-year-old sister has declined to add their mom ''because she thinks it is not cool.''
Lakeshia Poole, a 24-year-old from Atlanta, says ''my Facebook self has become a watered down version of me.'' Worried about older adults snooping around, she's now more careful about what she posts and has also made her profile private, so only her online friends can see it.
''It's somewhat a Catch-22, because now I'm hidden from the people I would really like to connect with,'' she says.
Lauren Auster-Gussman, a freshman at Juniata College in Pennsylvania, says it's particularly awkward when one of her parents' friends asks to join her social network. She thinks Facebook should only be used by people younger than, say, 40.
''I mean, I'm in college,'' she says. ''There are bound to be at least a few drunken pictures of me on Facebook, and I don't need my parents' friends seeing them.''
There are ways around the problem.
It's possible on some sites, for instance, to limit what someone can see on your profile, though some users think it's a pain to have to deal with that.
''That is the beauty of Facebook and other online social networks. If you want to only interact with your peers, then you can adjust the settings to only allow that,'' says Katie Jones, a senior at Ohio Wesleyan University, who's studied ways prospective students use Facebook to contact students at colleges and universities they're interested in attending.
It's also possible to simply decline or ignore an adult's request to be an online friend. Or adults could back off and only use social networking to contact their own peers.
But it's not always so easy to relinquish that control, especially for parents of teens, says Kathryn Montgomery, the author of ''Generation Digital: Politics, Commerce and Childhood in the Age of the Internet'' and mother of a 14-year-old.
''As parents, we have to figure out where to draw the line between encouraging and allowing our teens to have autonomy, to experience their separate culture, and when we need to monitor their use of media,'' says Montgomery, a professor of communication at American University.
She says it's especially important to help young people understand that social networking is often more public than they think. Sometimes monitoring them is the best way to do that.
Sue Frownfelter, a 46-year-old mom in Flint, Mich., thinks it's less of an issue for parents who discover technology with — or even before — their children. Among other things, she has a blog, uses Twitter and has a Chumby, a personal Internet device that displays anything from news and weather to photos and eBay auctions.
Her children, ages 9 and 11, begged her to allow them to have a MySpace page, because she does. Instead, she suggested Imbee.com, a social networking site for kids that allows parental monitoring.
''I can't imagine my life without technology! It has truly become an extension of who I am and who my family will likely be,'' says Frownfelter, who works at a community college.
Still, in today's world, parents are finding that the urge to stake out technological turf is starting at a very young age.
Jennifer Abelson, a mom in New York, says her 2-year-old daughter asks every day if she can play on the '''puter'' on such kid-oriented sites as Noggin.com and Nickjr.com.
''She's constantly telling us 'I will do it!' and 'Go away!' if we try to interfere with her 'working,''' Abelson says.
''It's pretty amazing to see technology ingrained at such a young age. But I know she's learned so much from being able to use technology on her own.''