Growing trees in internet news groups and forums

We present an empirical study of the networks created by users within internet news groups and forums and show that they organize themselves into scale-free trees. The structure of these trees depends on the topic under discussion; specialist topics have trees with a short shallow structure whereas more universal topics are discussed widely and have a deeper tree structure. For news groups we find that the distribution of the time intervals between when a message is posted and when it receives a response exhibits a composite power-law behavior. From our statistics we can see if the news group or forum is free or is overseen by a moderator. The correlation function of activity, the number of messages posted in a given time, shows long-range correlations connected with the users' daily routines. The distribution of distances between each message and its root is exponential for most news groups and power law for the forums. For both formats we find that the relation between the supremacy (the total number of nodes that are under the node i, including node i) and the degree is linear s(k)similar to k, in contrast to the analytical relation for the Barabasi-Albert network.