NEW YORK — Facebook, the largest social network, said it earned $425 million, or 17 cents per share, in the July-September quarter, up from a loss of $59 million a year earlier. Revenue grew 60 percent to $2.02 billion, helped by mobile advertising revenue. Analysts, on average, forecast $1.91 billion, FactSet says. Mobile ads accounted for 49 percent of ad revenue in the quarter. In the second quarter, mobile ads were at 41 percent. The increase shows Facebook’s ‘‘mobile-first’’ strategy is paying off.