• by Laurie Sullivan , Staff Writer @lauriesullivan, August 8, 2013

Sixty-eight percent of CEOs have no presence on any social network such as Facebook, LinkedIn, Google+ and Twitter, but a study released Thursday compares the presence of those who do.

The research from Domo and CEO.com, which analyzes the social media habits of CEOs at Fortune 500 companies, found 28 Fortune 500 CEOs (or 5.6%) on Twitter -- up from 18 (or 3.6%) last year. Of those 28, 19 are active, defined as sending tweets with the past 100 days. They send an average of 0.98 tweets daily, compared with Twitter's active global users at about twice daily.

About 46.4% of the Fortune 500 CEOs have verified accounts, up from 22.2% last year. When Warren Buffett joined it didn't take long for his account to see explosive growth. CEO.com reported in a previous post that for every hundred of his tweets, Buffett would get more than a million retweets. He gained 24,000 followers in 24 minutes, whereas it took Oracle founder Larry Ellison about a day.

The fastest-growing CEO Twitter accounts in terms of followers belong to Warren Buffett, Rupert Murdoch, and Ralph Lauren. Hewlett-Packard's CEO Meg Whitman remains the only one who is losing followers.

The report also estimates the percentage of fake followers. Buffett has 22%; Murdoch, 20%; and Marissa Mayer, 18. Mark Zuckerberg holds the dubious honor of being one of the CEOs with the most fake followers -- at 30%, along with Donald Slager.

Although I won't detail each of the social networks, I will mention that the way CEOs use LinkedIn continues to change, but it does remain the most popular network among the group. The study attributes the change to LinkedIn's Influencer program. The four Fortune 500 CEOs ranking as influencers include Whitman, Jamie Dimon, Jeff Immelt, and John Donahoe.

When it comes to stagnant social accounts, Facebook comes to mind. There are 35 Fortune 500 CEOs on Facebook, down from 38, and many no longer use the site. And what about Google+? Well, it has five -- up from 4 last year.