Figure 1. Reply trees and user network.

A) The set of all trees is a forest. Each time a user replies, the corresponding tweet is connected to another one, resulting in a tree structure. B) Combining all the trees in the forest and projecting them onto the users results in a directed and weighted network that can be used as a proxy for relationships between users. The number of outgoing (incoming) connections of a given user is called the out (in) degree and is represented by k^out (kⁱⁿ). The number of messages flowing along each edge is called the degree, w. The probability density function P(k^out) (P(k^int)) indicates the probability that any given node has k^out (kⁱⁿ) out (in) degree and it is called the out (in) degree distribution and is a measure of node diversity on the network.