NEW YORK (Reuters) - Kentucky Senator Rand Paul is trailing in Republican presidential polls but he had a strong showing among millennial on social media during Tuesday night's candidates debate.

Republican front-runner Donald Trump dominated the debate conversation on Yik Yak, an anonymous-posting social media app popular with millennial age Americans between 18 and 29, but not necessarily in a good way. He was a topic in more than a third of the mentions regarding the GOP debate but only 14.8 percent of them were positive in nature.

Paul, who barely made it into Tuesday's main TV debate, was mentioned positively in 67 percent of the posts about him, according to Yik Yak data, followed by Florida Senator Marco Rubio with a rating of about 50 percent.

Trump, whose brash style has dominated much of the campaign leading to the November 2016 presidential election, was mentioned in more than 30 percent of the conversations on Twitter with the #GOPdebate tag, according to Thomson Reuters social media sentiment analysis tool.

Texas Senator Ted Cruz, who recently surpassed the billionaire developer in opinion polls in the early-voting state of Iowa, followed with 16 percent while Paul scored 11 percent.

But the most retweeted post on Twitter with the #GOPDebate hashtag came not from a Republican but Democratic presidential candidate Bernie Sanders, responding to some of the Republicans' stance on national security.

"Repeat after me," Sanders wrote. "We must combat anti-Muslim bigotry and all forms of discrimination in our country and in our world. #GOPDebate."

Former Florida Governor Jeb Bush, who did not have a significant social media presence heading into the debate, was fourth in terms of Twitter traffic with about 10 percent. But his mentions were mostly associated with his heated exchange with Trump, which turned out to be most of the most tweeted moments of the debate.

The debate, the fifth one for the Republicans, was the most talked-about event on social media since the first one in August, according to Crimson Hexagon, a social media data company.

There were about 1.6 million debate-related posts on Twitter on Tuesday night, the highest volume since Aug. 6 when the first candidates' debate took up about 2.2 million posts on Twitter, according to Crimson Hexagon.

The average volume of posts in previous debates had been about 1.1 million.

Another trending topic during the debate was "House of Cards," a political drama series by Netflix. The streaming service announced the start date of the series' fourth season by launching a fake presidential campaign ad for one of its protagonists, President Frank Underwood, played by Kevin Spacey.

(Reporting by Angela Moon; Data complied by Connie Yee, Thomson Reuters F&R; Editing by Bill Trott)