Social Network Analysis of Twitter... you had to know it was coming

You had to know this was coming - after a mobile and Facebook post, what was left? This is probably the most interesting/ counter-intuitive of the 3.

What is Twitter, a Social Network or a New Media? [Haewoon Kwak, Changhyun Lee, Hosung Park, and Sue Moo] mined ~42mm profiles, tweets, and trends to better understand the nature of Twtter. The broke it into 3 parts:

1. Network Analysis - understanding the structure of the Twitter network.
2. Popularity Analysis - based on # of followers, pagerank, and retrweets
3. Information Diffusion - how (re)tweeting diffuses through the network. 

Here are the major outcomes: 

1. There is basically (basically) a 1-1 correlation with # of tweets, and # of followers/ followings. Tweet more, get more followers.
2. Low reciprocity. Due to the asymmetrical nature of twitter (ie I can follow you without you following me back), only 78% of links are one way. 
3. Degree of separation: on twitter, there are 4 degrees of separation. This is really unintuitive at first due to the directedness of the network, but if you consider the "super nodes" on twitter (eg Oprah), this makes sense. Conversely, on facebook, most poeple can't be friends with Oprah. 
4. Homophily: People who have a lot of followers tend to be friends with people who have a lot of followers. The more followers you have, the more likely your friends are in other timezones. 
5. User Popularity: Ranking by followers is interesting, but they're actually not generating the most retweets (this is a better measure of influence). 
6. Trending items vs google: items stay trending on Twitter longer than Google due to the retweeting phenomenon.Most active periods are less than a week, but 31% are 1 day long.
7. Retweet impact: (this is weird) regardless of how many followers you have, if your tweet is retweeted, 1000 people will see it. Of course, if you have more followers, your tweet is more likely to be retweeted, but a retweet view remains constant at 1000 incremental people.
8. On average, if they happen, first retweets occur ~1 hour after the tweet, 2nd - 6th occur within 10 minutes. Crazy diffusion rate.

Basic Social Network Analysis Criterion

Just finished two interesting papers which analyze social networks: Planetary-Scale Views on a Large

Instant-Messaging Network (Leskovec, Horvitz) and Statistical Analysis of Real Large-Scale Mobile Social Network (Zhengbin Dong, Guojie Song, KunqingXie, Ke Tang, JingyaoWang).

The former was an a an analysis of a month's worth of MSN Messenger traffic and network structure. The latter, an analysis of chinese phone log and corresponding network structure. 

Though the results were interesting (I won't share them here), I was actually looking for the criterion they analyzed: 

• Degree: simply put, the number of connections a user (node) has. 
• Shortest Path: the fewest number of users between two users. 
• Diameter: the largest shortest path in a network. 
• Clustering Coefficient: the ratio of actual connections a user has to potential connections. Measures  the transitivity of a network (ie the propensity for your friends to also be friends themselves).
• Betweenness Centrality: the ratio of the count of shortest paths (between user A and user B) that pass through a user (user C) to all shortest paths (between user A and user B).
• K-Core Distribution of Component Size: gives us an idea of how quickly the network shrinks as we move towards the core. Or, how large (number of users/ nodes) is the core component when a constraint of the minimum degree (k) is applied. (ie for a network where nodes have degree, k >20, how many total nodes in the component?)

Most of these characteristics are represented as a distribution (ie what is the degree distribution of all nodes in a network?) and tend to provide insight into the stability and density of a network. For example, a network with a higher-than-average skewed degree distribution (ie people have a lot of friends), will tend to be more stable (ie be more resilient to the k-core test), have shorter paths (on average) and therefore a smaller diameter, will be clustered more, and have higher betweenness centrality. 

This is really nerdy stuff...