I sat down Tuesday afternoon in Mountain View, Calif., with Dan Nye, the newish CEO (he joined earlier this year) of LinkedIn. That’s the company that is like Facebook for grownups, a businessperson’s social networking site. Nye’s looking for press because LinkedIn plans to unveil some nifty new features on Dec. 10. (I got a look, but agreed not to divulge anything yet.) I was interested in hearing what he had to say, in part because of the rumors flying around that LinkedIn plans to sell the company early next year to News Corp. (NWS)

The buyout gossip began with an item last week in the UK version of TechCrunch. Never mind that LinkedIn founder Reid Hoffman (a made man in the PayPal mafia and a buddy of mine) categorically denied the rumor in the Daily Telegraph. Anything that suggests that Rupert Murdoch would expand his social-networking empire is sure to set tongues wagging. Breakingviews.com wrote an intelligent summary of why a LinkedIn acquisition would make sense, largely because of the opportunities to leverage LinkedIn’s tools with the Wall Street Journal readership.

Not surprisingly, Nye didn’t deny that News Corp. made an offer for his company. Instead, he said that when he joined the company he told the board — comprised of Hoffman, Sequoia’s Mark Kvamme and Greylock’s David Sze — that he was only interested in taking the job if the goal was to “go long.” But is he selling out anyway? “We’re excited about building this company,” said Nye. “It would take a helluva lot to get us off that path.” Does that mean $1 billion? “A lot more than that,” said Nye, who worked at Procter & Gamble (PG), Intuit (INTU) and Advent Software (ADVS) before joining LinkedIn.

LinkedIn clearly is playing to win. The company has mushroomed from 60 employees when Nye joined in February to almost 200 today. At the time, LinkedIn had 9 million members; today it has nearly 17 million. Nye predicted revenues will range from $75 million to $100 million next year.

LinkedIn has the virtue of having survived adversity. Before Facebook and MySpace existed — back when Friendster was hot — LinkedIn was just getting going. It’s still going. Independent or part of News Corp., it’s fun watching this plucky company succeed.

I saw something more than a little scary last week at Google (GOOG): A calm, confident, friendly management team that seemed more comfortable in its own skin than I’ve ever seen them.

For the first time, Google invited a handful of journalists to its annual Zeitgeist conference for advertising partners. Afterwards, Larry Page, Sergey Brin and Eric Schmidt held an on-the-record chat with us over sandwiches. They talked about their interest in wireless spectrum. They fretted that their biggest challenge (still) is managing their growth. They even showed their sense of humor. When I noted the unusual stability of the top executives beneath the ruling troika (as a prelude to asking if that stability would continue), Page quipped, “Emotionally or physically?” More seriously, he predicted continued stability and suggested a leadership training program is helping. (The word is that many of Google’s “economic volunteers,” a term that’s actually used within the company, will be retiring soon and that turmoil will hurt.)

The arrogance remains, of course. Schmidt held forth on how much the company is doing to address the concerns that caused Viacom (VIA) to take Google to court over YouTube’s policies regarding content it doesn’t own. He said filtering technology is in “various stages of rollout,” as if that were good enough. He said Viacom “rushed” into litigation. He obviously has the luxury of knowing the suit has done nothing to blunt YouTube’s advance.

On the subject of social networking, and Facebook in particular, they made it very clear just how interested Google is in getting into the game in a more meaningful way than its Orkut service. (Read my colleague Josh Quittner for a contrary view on how much Facebook worries Google.)

Bottom line: From my perch, these guys were cool as cucumbers. Genuinely relaxed, engaged and at the top of their game.

By the way, Google reports earnings Thursday. The company’s worth $200 billion. And its founders give off the vibe that they’re just getting going. As I’ve written in the past, Google’s management isn’t perfect. Its previous quarter was sloppy. My gut tells me this one won’t be.

I didn’t attend Zuckfest in San Francisco Thursday. (I was busy, not uniterested.) But I did read David Kirkpatrick’s comprehensive report on what Facebook is up to with its new platform concept, as well as a whole bunch of other descriptions of the attempt by CEO Mark Zuckerberg - whom I’ll always remember for his one-of-a-kind business card - to create Macworld-like drama the way Apple (AAPL) CEO Steve Jobs does. (Particularly worth reading is a contrarian take by paidContent.org that throws a fair amount of cold water on Facebook’s dramatic announcement.)

What interests me here is whether anyone over about 25 will really use Facebook, including folks who use it in college and then go out into the real world. Last fall, when Facebook started expanding to allow corporate e-mails to be used to establish accounts (around the same time the company reportedly turned down a billion-dollar offer to be bought by Yahoo (YHOO)), I asked Facebook to start one for Fortune’s editorial employees. I then invited everyone on staff to be my “friends.” Three accepted, and I’m not naming names, nor did I take the rejection personally. It was more that no one seemed to care. Since then I’ve been steadily getting invitations from all over the place for people to be my “friends,” many from people I’ve never met or met only once. My hunch is that adults are finding out about Facebook and then inviting everybody they can think of. But will they actually visit the site and see who is “poking” them? I seriously doubt it. I don’t use LinkedIn much either, but I know that lots of people do, and I understand why: It’s got content that helps them do their job. And even then, it’s not like you’re going to spend a ton of time on LinkedIn, the main premise behind Facebook and News Corp.’s (NWS) MySpace. Professionals get in and get out. They’re too busy to do otherwise.

(Will adults use Facebook? Have your say in this poll.)