"A few Chirps about twitter" gives valuable insight into how we use the application and why we use it.
It is a paper written by Balachander krishnamurthy (AT&T Labs), Phillipa Gill (Uni Calgary) and Martin Arlitt (HP Labs - Uni Calgary)
"Our goal is to characterize a novel communication network in depth, its user base and geographical spread, and compare results of different crawling techniques in the presence of constraints from a generic measurement point of view".
They gathered 3 datasets covering nearly 100,000 users. Detailed information was gathered on each user and the list of users they were following. They say that relationships in Twitter are directed but that there is no way of gathering the set of reverse links: information on the set of users following a user.
They collected data at specific times of the day and extracted the users that posted at these times - they collected data from each user and a partial list of his/her followers.They gathered data for 3 weeks.
"During this process the median number of users followed by the previously crawled users, m, was tabulated. To further the crawl the first m users followed by the current user would be added to the set of users to crawl."
It focused on current active users who continually post a series of 20 or more updates. Details were collected on each user
They used a Random walk with backtracking to collect the data. They only considered once child of each node.
Distinct classes of users were identified:
Broadcasters - They follow few but have a large number of followers
Acquaintances - they reciprocate the follow (so have an even spread of following-followers)
Miscreants - spammers or stalkers who contact everyone they can to get followers
How did users access Twitter:
61% use the web, 7,5% mobile, 7.2% IM, 1.2% Facebook, 22.4% custom applications
Highly popular users update their status very often, generally those with more than 250 followers updated a lot more often than others.
There is a lot more information and analysis present in the paper, give it a read, it's very accessible.