Shares of Facebook Inc fell more than 2 percent in early trading on Tuesday after the two founders of photo-sharing app Instagram left the social networking giant under unexplained circumstances.

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Analysts said the departure of Kevin Systrom and Mike Krieger may have been the result of friction with Chief Executive Officer Mark Zuckerberg over how Facebook's fastest-growing revenue generator is run.

"Our sense is the duo may have wanted to run Instagram more independently than their parent company wanted," said Scott Kessler, an analyst at research firm CFRA.

"We think (the) departures are a notable negative for Facebook."

The sudden loss of the pair follows the departures of WhatsApp co-founders Jan Koum and Brian Acton and a reshuffling of Facebook's executive ranks earlier this year.

A Bloomberg report said Systrom and Krieger had been frustrated by a rise in the day-to-day involvement of Zuckerberg, who has become more reliant on Instagram in planning for Facebook's future.

Facebook's shares were down 2.4 percent at $161.51 in early trading, knocking more than $11 billion off the stock's market value.

"To the extent that their departures represent Zuckerberg exercising more power and being less accountable, such a development would underscore the need for an independent board chair," said Jonas Kron, senior vice president at Trillium Asset Management.

The institutional investor, which holds more than 52,000 shares in Facebook, urged Facebook in July to appoint an independent board chair to oversee management.

Systrom wrote in a blog post on Monday that he and Krieger planned to take time off and explore "our curiosity and creativity again".

Zuckerberg described the two as "extraordinary product leaders" and said he wished them all the best and was looking forward to seeing what they build next.

Facebook bought Instagram in 2012 for $1 billion. Instagram had been hailed in Silicon Valley as a flashy acquisition done right, with the team kept relatively small and Systrom having the freedom to add features such as peer-to-peer messaging, video uploads and advertising.

Instagram has over 1 billion active monthly users, a sharp rise from the 30 million users when Facebook bought the app.

Facebook's shares are currently down about 6 percent this year, following six years of stellar gains.

Concerns over the fallout of the Cambridge Analytica privacy scandal and signals that a rise in costs would hurt Facebook's margins for years, fueled the biggest one-day wipeout in U.S. stock market history in July.