In a New York Times Op-Ed last December, Tim O’Reilly fantasized:

Imagine, for a moment, that Verizon were to think like Google or Amazon. It could give you access to your entire call history, every phone call you have sent or received, not just your last 10 phone calls. It might build an address book for you based on everyone you had ever talked to, with top results for the numbers you call most often.

And what if this phone company opened up its databases to developers of software applications? We could soon see mash-ups of your call history with the address books from your personal computer, your telephone and your social network. Now imagine a user community turned loose to annotate that data.

Little did O’Reilly know when he wrote this that a then-stealth startup called Skydeck was figuring out a way to do just that. Skydeck launched in private beta last March with a very basic service that marries your address book to your cell phone bill so you can see your real social network based on who you call the most. Up until now, people in the private beta could see their cell phone social network, but that was it. They couldn’t connect with anyone else using the service.

But starting today, members can opt in to connect their social networks with other friends who are also using Skydeck. What makes this interesting is that they can see the strength of their connections to each friend, as well as how strongly connected their friends are to other people. Skydeck measures the strength of a relationship based on the frequency and volume of calls between two people, how recent the calls were, and whether the calls were reciprocal or one-sided. Skydeck rolls up all of this data and represents the overall strength of a relationship as rising signal bars.

Now, there aren’t that many people using Skydeck yet because it is still in a closed beta. (We have 700 more invites for readers who apply here and mention “TechCrunch.”) But that’s not stopping Skydeck CEO Jason Devitt from opening up APIs to the Skydeck service so that other Web developers can tap into this new source of social data.

Exactly what kinds of apps will Skydeck’s APIs make possible? I asked Devitt, and he came up with the following, which are not half-bad (all are hypothetical, but technically possible):

Top 10 Apps That Could Be Built With the Skydeck APIs (my title)

1. You could write a plugin for Outlook or use Gmail’s API to display the last time you spoke to someone [on the phone] when you bring up an email from them.

2. Or you could go further and create an app showing in one place the history of your email, IM, Skype, and cell phone conversations with all your contacts (the cell phone is the missing piece – all the other data is already accessible).

3. You could write an app displaying every call longer than one minute in iCal at the date and time it took place, so that [a record of] all your calls appear in the same place as your in-person meetings.

4. 37Signals could add a note to the Highrise page for every call you make to a contact tagged “Business” in Skydeck.

5. RescueTime could display all the hours you spend on the phone alongside the applications you use and the web sites you visit.

6. FreshBooks could break out calls with clients on invoices for their customers.

7. LinkedIn could use ranking data to show which of the five people that we both know is best placed to introduce you to me.

8. You could write an app to bring all this data back to your smartphone. We will target some phones ourselves, but we can’t address every platform and we won’t stop anyone from trying.

9. You could write an app showing which of your Facebook friends you text [or call] most often. (You’d have to match on name because Facebook doesn’t disclose email addresses etc., but that’s not so hard.) Or use our measure of reciprocity to poke the friends that never call you back.

10. You could throttle tweets to your cell phone based on how many text messages you have left in your plan. (We track how many minutes and text messages you have left each day).

Integration with Salesforce is another obvious one. What apps would you build, or want to use, that ties into your cell-phone social network?

“Your most important social network is the one in your phone,” says Skydeck CEO Jason Devitt. With Skydeck, he hopes to do the impossible: turn your cell phone bill into something useful. You give Skydeck the login for your mobile phone account. It scrapes the page and matches the calls with your address book, turning each phone number into a name so that you can sort your phone bill like e-mail. (It’s like Xobni for your cell phone records, see screen shot below). Skydeck tells you who your most important relationships are, based on how often you call someone or they call you. It even tells you which way the relationship is skewed.

The private beta launched today. To get an invite, be one of the first 500 people to sign up here (enter “TechCrunch” in the box labeled ‘Where did you hear about Skydeck?”).

Says Devitt:

We’re trying to introduce information transparency into a market where there is none. All your call records are in your cell phone. We have figured out how to unpack that information, match it to your address book and present you with who your most important relationships are.

Once Skydeck unpacks this information you can start to do interesting things with it, like add tags to calls. Tag all you business calls on your cell phone bill, and you’ve got an expense report. You can sort by name, date, call length, or most expensive call. Skydeck lets you search your call records as easily as you can your e-mail. There is also a Firefox plug-in that keeps tabs on how many mobile minutes you have left this month.

Skydeck raised $1 million in February from angel investors. The service will be free for consumers. Devitt plans to make money by charging small businesses for premium services such as expense management. He also sees an opportunity for promoting other voice-related services such as voicemail transcription.

Devitt plans on adding many more features and services in the future, such as a reverse lookup for numbers not in your address book. The real potential for this, however, is to take that rearranged address book and import it back into your cell phone. “Alphabetical order is a stupid way to organize your address book,” says Devitt. (Unfortunately, you cannot do this yet). Devitt also wants to let people marry the social relationship map Skydeck culls from your cell phone data with your online social networks. Then you could see at a glance who your real friends are. You know, the ones you actually talk to.

Keep an eye on this one. The last startup Devitt founded was Vindigo (mobile city guides). He is a feisty entrepreneur, as you can see from this video below showing him testifying before Congress last September on the importance of open access for wireless networks: