NEW YORK – Facebook’s stock gained the most in a single day Wednesday since it began trading in May, a sign that the social media company’s complicated relationship with Wall Street may be getting brighter.

It’s been a rough five months since the social network’s initial public stock offering, and it’s too early to tell whether investors’ optimism is here to stay. But on Wednesday they latched on to clear signs of growth in the company’s third-quarter earnings report. Several analysts upgraded the stock.

Besides posting quarterly results that inched past Wall Street’s expectations, Facebook on Tuesday also gave details for the first time on how much money it made from mobile ads. This has been a concern since before its IPO. Although the majority of 1 billion people who use Facebook each month now access it using a mobile device, the eight-year-old company was created in the age of desktop computers, for Web pages. Facebook now calls itself a “mobile-first” company, but it only started showing mobile ads earlier this year.

On Tuesday, Facebook said that nearly $153 million of its $1.26 billion revenue came from mobile advertisements. The rate of advertising revenue growth also accelerated since the second quarter.

Shares of Facebook Inc., which is based in Menlo Park, Calif., rose $3.73, or 19 percent, to close at $23.23 on Wednesday. It’s by far the stock’s biggest one-day gain, in percentage terms, since Facebook went public on May 18. Still, shares are still off 39 percent from the company’s IPO price of $38.

Tuesday’s strong report doesn’t mean Facebook is out of the woods. Later this month, and then again on Nov. 14 and Dec. 14, more employees will be allowed to sell their holdings as restrictions on selling, typical in the months after an IPO, expire. If shares flood the market on those days, it could weigh on Facebook’s stock.