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...
