The Twitter-verse is a complicated web of friends, followers, re-tweets and hashtags. It can be a headache to follow what’s really happening with your own tweets, let alone the whole Twitter eco-system.

We took a look around the web for some interesting ways to visualize Twitter – in graphs, charts, or more abstract images. Here are three of the coolest Twitter visualization tools to give you a break from all that 140-character-sized text.

Visualization number one is called the Twitter Friends Network Browser. It is a simple app, but it’s interactivity makes it ultra-fun to play with. You start by typing in a username of someone on Twitter (I chose myself, but you could be less egotistical and try someone you follow or a public figure). The app then loads your Twitter profile pic and latest Tweet, and surrounds you with a wheel of your friends – with spokes denoting a connection.

It’s fun to dig deeper into the connections, by clicking on one of the people you follow. A new wheel of those who they follow will surround them. I’m not sure just how many different wheels you can have going at once, but I made it to five before it got a little to busy for my brain to comprehend.

Want to know everything about your Twitter habits? Well the next visualization on our list, TweetStats, will show you in graph and chart form. You can visualize how many Tweets you’re clocking aggregated over the past month or hour, who you reply to most often, who you re-Tweet, where most of your Tweets are coming from and more.

Are you a Monday morning tweeter? Or do you burn the midnight oil and find most of your witticism comes out on Saturday nights? You can find out all about your Twitter habits with this cool visualization. And it’s fun to try out people other than yourself, too, to see how they interact with Twitter.

MentionMap shows a visualization of mentions – the hashtags and users that a particular Twitter user mentions most often in recent Tweets. I took a look at Barack Obama’s Twitter, and found some interesting mentions – TheDailyShow and TheDemocrats were both mentioned 3 times, only beaten by timkaine, Governor of Virginia and head of the DNC.

This visualization lets you explore the data by clicking on a user mentioned by your initial subject and shifting the spokes over to the new user and his or her mentions. Take a look at the Barack Obama MentionMap below:

These visualizations can display your Twitter data in a more interesting, easy-to-understand way – after all, humans are visual creatures.

Have you found any cool Twitter visualization tools? We’d love to get our hands on more! Let us know in the comments.