Wolfram Alpha has added some cool new tools to its Personal Analytics for Facebook tracker while tweaking some existing features from the first release(Opens in a new window), which went live last August.

I tooled around on the new version Thursday morning and found a lot to like. Among the new and improved features, the additional capabilities added to the Facebook visualization tool stand out as particularly fun and interesting.

To start with, Wolfram Alpha presents your Facebook network in color-coded clusters of individual friends represented as little circles, which can be moused over to bring up their identities. The fascinating thing here is that you get an immediate idea of the various and more or less distinct social groupings to which you belong —Wolfram Alpha also breaks this data out in list form after generating your personal analytics.

Wolfram Alpha’s visualized Facebook friend map.

So for example, my Facebook network contains five big clusters of friends, breaking down roughly as family, work colleagues and contacts, political allies, friends from my years in Thailand, and the biggest of all, friends from high school. That’s probably way over-inflated courtesy of a big Facebook push by the organizers of my 20th anniversary high school reunion a few years back.

You can also refine that network visualization using scroll-down menus added to the new version of Personal Analytics for Facebook—I’ve placed some images of different ways to do that in this article, which you can click to enlarge.

As you play around with the network visualization feature, breaking out particular friend groupings by age, gender, locale, etc., you may find that the most intriguing thing is the new ability to isolate and identify friends who link together your various social clusters and the “lone wolves” with whom you have few or no mutual friends.

Wolfram Alpha Personal Analytics for Facebook.

Wolfram Alpha certainly appears to have anticipated that this would be a popular use of the tool. As John Burnham explained in an official blog post(Opens in a new window) post introducing the new Personal Analytics features, the answer engine even cooked up some descriptive labels for friends that play particular roles in your Facebook network.

“One of the most shared pods from our first release was our colorful social network visualization. We’re extending this idea to help you better understand how your social network fits together. To start with, we’re showing you a new visualization that highlights friends based on the way that they fit into your network,” Burnham wrote.

“Let’s take an example. Say you’re a college student. You might have a group of friends from college, and another group from your old high school. If you’ve got any college classmates who also went to your high school, we might label them on your report as social connectors, because they connect two otherwise separate groups of your friends.”

Wolfram Alpha Personal Analytics for Facebook.

All told, there are five types of friends Wolfram Alpha highlights for the specific “network roles” they play—insiders, outsiders, neighbors, gateways, and connectors—each of whom is identified in Personal Analytics for Facebook in the visualization tool and in a listed ranking.

“Social insiders and outsiders are opposites: a social insider has a lot of friends in common with you (e.g. your girlfriend since freshman year); conversely, a social outsider is someone with whom you have few or no mutual friends (e.g. that girl you met horseback riding in Romania),” Burnham explained. “Social gateways and neighbors are also opposites: a social gateway contact has a lot of friends that are outside your network (e.g. the editor of your college newspaper), whereas a social neighbor has few friends outside your network (e.g. your identical twin).”

Other metrics and tracking tools generated by Personal Analytics for Facebook include a ranking of the most common first names among your friends, a useful clock that tells you what time it is where your various friends live, the “geographic extremes” of where your most far-flung friends reside, a more easily readable app activity tracker, and, of course, the word cloud.

The word cloud sifts through your own Facebook wall posts to create a visual picture of the words you’re using most frequently in your pronouncements to your social network. Word clouds aren’t a new thing, but they can certainly produce some head-scratching results, as evidenced by the one Wolfram Alpha generated for me, below.

My mom will probably be happy to see that she features prominently in my word cloud; meanwhile, I’m wondering why I apparently complain about being “bored” with all the manufactured ennui of a texting tween. Also, Jägerbombs? Yeesh.

If you want to run your own Facebook profile through Personal Analytics for Facebook, it’s very easy to do—simply get started by clicking over to Wolfram Alpha’s launching page(Opens in a new window) and follow the simple instructions, which include signing into Facebook if haven’t already, allowing the Wolfram Alpha app access to your Facebook activity, and registering for a free Wolfram Alpha account.

For more from Damon, follow him on Twitter @dpoeter(Opens in a new window).