Developers of the next-big social networking application stand a greater chance at skyrocketing success if Hollywood stars and big media go gaga over it, according to an analysis of Twitter's meteoric rise in popularity.

Data collected on the number of users adopting the microblogging service in its early years (between 2006 and 2009) show that it first spread gradually via traditional social networks — real-world friends, work colleagues, neighbors — then took off when media stars started to gather their flocks.

 

---

"The first big run up in the number of Twitter users corresponded to the months that Ashton Kutcher was trying to be the first one to a million followers," Jameson Lawrence Toole, a graduate student at the Massachusetts Institute of Technology, and co-author of the study, told me today.

 

 

The Hollywood actor, who is most recently in the news for his recent divorce with actress Demi Moore and starring role in the hit TV series Two and a Half Men, touted his Twitter flock on Oprah Winfrey's daytime talk show. And that's also when Oprah herself sent her first tweet.

"The most number of people ever signed up for Twitter during that week," Toole said.

From there, Twitter's rise was unstoppable. News reporters wrote about Kutcher and Oprah and more people signed up for Twitter. More media personalities wrote their own stories about sending 140-character tweets. More people signed up. More stories, more users.

While the data isn't all that surprising, it suggests a new way for researchers to model the power of media influence in their analyses of what drives a company to success, according to Toole.

In traditional models, he said, the role of media is considered a constant across time. What the Twitter analysis illustrates is the existence of a feedback loop present in today's media. "The more people sign up, the more news articles are written, and then more people sign up," he said.

The effect has been named elsewhere as the Oprah Effect, which is particularly prevalent in book sales. Aspiring authors know that if the talk show host picks their book for her monthly book club, for example, a spot on the best seller list is almost certainly in their future.

The comedian Stephan Colbert has a similar effect, known as the Colbert Bump, which is particularly effective for politicians, according to Toole.

Given the analysis of Twitter data from its early years, the power of big media stars seems to apply to Internet-based applications as well. So, if you want millions of users to use your app, make sure a big name pitches it, preferably in a quasi-viral way. That should mean success, according to the new model.

"What we can't model is if Oprah is going to pick up your Web service," Toole noted. 

More stories on Twitter and the power of media:

• Turns out Twitter is more than Ashton Kutcher
• Oprah's magic helps small businesses, ready or not
• Science confirms the 'Colbert Bump'
• Human brain limits Twitter friends

---

The study is scheduled to appear this month in the journal PLoS One.

John Roach is a contributing writer for msnbc.com. To learn more about him, check out his website. For more of our Future of Technology series, watch the featured video below.

Yes, some people have millions of followers on Twitter. Lady Gaga was the first to hit 10 million. Justin Bieber, Barack Obama, and Britney Spears are close behind. But how many of these followers are really their friends? Our brains, it turns out, limits that number to around 150.

In the early 1990s, British anthropologist Robin Dunbar figured out that the human brain can only accommodate between about 100 and 200 stable relationships. That's essentially because we have so much to do in so little time that our brains limit the number of relationships we can manage.

---

But with the rise of social media, this premise, at a glance, seems to be changing. Many of us maintain hundreds, if not thousands, of connections on sites such as Facebook, Twitter, and Foursquare. Could it be that these networks are lifting our social capacity?

To find out, Bruno Goncalves and his colleagues at Indiana University gained temporary access to the Twitter "firehose," as they call it, and analyzed 380 million tweets sent by 3 million tweeters over a period of four years.

To be a friend instead of just a follower on Twitter, for the study at least, Goncalves's team worked out a formula that measures increasing bonds by the number of conversations, or exchange of tweets, between individuals.

A lot of tweets between you and Lady Gaga? Cool. You might be a true friend, not just one of her millions of followers. 

What the researchers found was that when a person opens an account on Twitter, they have few friends and few interactions with them but as time goes by, stable users get more and more friends. Then they get overwhelmed. 

"Eventually, a point is reached where the number of contacts surpasses the user's ability to keep in contact with them. This saturation process will necessarily lead to some relationships being more valued than others," the researchers write in their study posted on the preprint server Physics arXiv. 

That point, it turns out, is between 100 and 200, as predicted by Dunbar.

"This finding suggests that even though modern social networks help us to log all the people with whom we meet and interact, they are unable to overcome the biological and physical constraints that limit stable social relations," they conclude.

More stories on social networks and friends: 

• What evolutionary psychology says about social networking 
• Most replace half their of their friends every 7 years 
• When you don't want to be Facebook friends 
• Decade of tweets, friends and hands across Web 

---

John Roach is a contributing writer for msnbc.com. Connect with the Cosmic Log community by hitting the "like" button on the Cosmic Log Facebook page or following msnbc.com's science editor, Alan Boyle, on Twitter (@b0yle).