A few months ago, I did some research into visualizing how a story spreads across the Twitterverse and how that spread could be visualized.
Using a combination of the Twitter API, the TweetMeme API and the Processing visualization library, I was able to graph the spread of a handful of popular links.
In the TweetMaps below the circles represent each user who ReTweeted the link, they're bigger or smaller based on the number of followers they have. People who are following accounts that Tweeted the link before they did have lines drawn to the accounts they're following (and could have "caught" the link from).
The graphs show the first wave of Tweets of each link (generally the first few hours). When you see a number of circles extending horizontally across the graph that means that those accounts all Tweeted the link very close together in time.
The first example is a post on the HubSpot blog. You'll notice there's a line of accounts that posted the link at very similar times. This is because there are a number of automated Twitter accounts that post every link on the HubSpot blog RSS. You'll see this pattern again in the examples below. You'll also notice that there is a high amount of variance in the size of the circles, indicating that the people who Tweeted the link have varying amounts of followers, and there is a high amount of interconnectivity between them as well.
The next example is from celebrity gossip blog TheFABlife. The difference is striking, other than a single, highly followed account (which is probably the blog's own official account) all of the other accounts have few followers. This is a good indication that this link's audience is much more "mainstream." Again notice the high level of interconnectedness visible.
Now let's look at a TweetMap of a link from Seth Godin's blog. You'll notice there isn't one big account that starts the chain (since there is no active, official Seth Godin Twitter account). There is a lower amount of interconnectivity present than in the previous examples, and most Tweeters have low numbers of followers.
The above example is from MSNBC's site. There are very few connections between ReTweeters, and there are a few very large accounts amidst mostly low-follower accounts. The large accounts are probably official MSNBC accounts.
An example from FoxNews tells the story of a community with a high variation in follower counts and lots of inter-connections.
An example from Alternet.org shows a set of accounts with lots of followers and a moderate amount of connection.
The final example, from TechCrunch, shows the main Techcrunch account followed by a large number of low-follower accounts. It also displays lots of connections and a large automated Tweeting line.
Marketing Takeaway
The internet now gives marketers a way to map word-of-mouth that was previously impossible. Take the time to understand how your content as well as your competitors content spreads online. Look for opportunities to optimize the word-of-mouth spread of your content on Twitter and other social networks.