A study of millions of Facebook users on Election Day 2010 has found that online social networks can have a measurable if limited effect on voter turnout.

The study, published online on Wednesday by the journal Nature, suggests that a special “get out the vote” message, showing each user pictures of friends who said they had already voted, generated 340,000 additional votes nationwide — whether for Democrats or Republicans, the researchers could not determine.

The scientists, from Facebook and the University of California, San Diego, said they believed the study was the first to show that social networks could have at least some impact on elections, and they added that the findings could have implications far beyond voting. For example, research is now being conducted on the use of social networks to help people lose weight.

Significantly if not surprisingly, the voting study showed that patterns of influence were much more likely to be demonstrated among close friends, suggesting that “strong ties” in cyberspace are more likely than “weak ties” to influence behavior. It also found an indirect impact from the messages: friends of friends were influenced as well.