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Today, Facebook has demonstrated why you will never leave it. You can live without the Newsfeed. You can live without the Timeline. You can live without knowing which of your smug-smirking friends has posted a photo of their feed from a tropical beach. But you can’t live without its connections.

Facebook is still known as a “social network,” but its true power lies in being a “connections network.” As a destination site for finding out what your friends are up to, it is still compelling, but we have already seen how its primacy in that position is not entirely invulnerable. Twitter, Instagram, Pinterest, Google+, and mobile messaging services such as Snapchat, WeChat, and KakaoTalk have all succeeded in stealing away some of the social messaging attention market. Our own Kevin Kelleher has written about Facebook’s growing “silent majority” – people who won’t leave the site, but who certainly don’t go there everyday.

But none of those sites are even close to rivalling Facebook’s true, perhaps unstoppable, advantage: Its global network of 1 billion users. In a sense, Facebook has created a new World Wide Web. The Internet is still a massive network of connected machines, but Facebook has made it into a massive network of connected humans.

We’ve said before that Facebook’s primary failing as a public company is that it hasn’t yet leveraged this power in the right way. Graph Search, which Mark Zuckerberg unveiled today at a much-Tweeted press conference, may be one of the first real glimpses of what that would look like.

Want to find a friend who lives in Los Angeles and likes to surf? Go to Facebook.

Need to find a restaurant in Amsterdam that people who identify as foodies like? Maybe you should try Facebook before you try Yelp.

Only interested in hooking up with someone who is single, likes Coldplay, and went to an Ivy League school? Well, you’re an asshole, but Facebook will still look after you.

This is not too different from what has made LinkedIn successful. Few people other than recruiters use it everyday. But anyone serious about their career should have a well-groomed LinkedIn page with a decent graph of professional connections. You may never need it, but then one day you might get laid off and suddenly LinkedIn is the most important site in your life. LinkedIn has balked at this description, but its power comes more from being a career AAA card than a daily-use a social network.

As a reporter, I’ve always found Facebook most useful as a rolodex, not only to keep track of my friends, but also to keep track of contacts, find out more about them, and to send messages to people whose other contact details I don’t have. If it weren’t for the value of this rolodex, I might have left Facebook years ago. Now, thanks to Graph Search, Facebook is like a rolodex on whatever Lance Armstrong was taking when he won seven Tour de Frances. Zuckerberg knows that, which is why Facebook has set up a special page to show just how damn useful Graph Search can be for journalists.

Journalists, however, merely provide an easy way to demonstrate just how valuable access to such a vast network of people can be. In the promo video for the launch of Graph Search, Facebook product director Tom Stocky says it helps “make your community feel a bit smaller; make your world a bit smaller.”

Right there is Facebook’s real value proposition. It stitches together disparate chunks of the world’s population, makes sense of them in categories, and then makes them accessible to strangers. This convergence of humanity increases and speeds up the flow of information, and now Graph Search helps unlocks the latent potential in human relationships that otherwise might not have happened. Keep in mind, also, that, per Zuckerberg, Graph Search is only in Version One of beta. The capabilities Facebook showed off today are just the beginning. (One would hope a mobile version might come at some point.)

Graph Search is also a major blow in what Sergey Brin sees as the war between the “closed” and “open” Web. Amid all the obsessing about Facebook’s stock price, display ads, Timeline redesign, and Newsfeed noise, it can be easy to overlook the fact that Facebook has essentially built an alternative universe that is serving as the fabric on which the “closed Web” is being built.

In the closed Web, companies have ready access to your identity and data, and you have an easy sign-on option to their wares. Their products sit on a foundation made up of Facebok’s web of connections, but Facebook gets to own that platform and, effectively, the data and media within its walls. The likes of Zynga, Spotify, and, more importantly, you must then bend to its terms and conditions in exchange for access to that immense database of 1 billion people.

That would appear to leave Google with the opportunity – or responsibility? – to serve as the social fabric on which the “open Web” is built. Over at Fast Company, Dave Llorens has argued that Google+ will prevail with its attempts to add a “social layer” for the Web rather than build a Facebook-like closed garden. That might ultimately prove the more noble approach, but so far it is the losing one. Facebook has 1 billion users, and it’s not going to lose many of them any time soon. Google also runs the risk of compromising its “openness” by being overly agressive with its ambitions for Google+. Meanwhile, Graph Search has just made “Search Plus Your World” look like a piffling after-thought.

Facebook’s mission statement is to “make the world more open and connected.” Today, it delivered on half of that promise. The other half will be up to someone else.