The Metabolism and Growth of Web Forums

We view web forums as virtual living organisms feeding on user's clicks and investigate how they grow at the expense of clickstreams. We find that [Image: see text] (the number of page views in a given time period) and [Image: see text] (the number of unique visitors in the time period) of the studied forums satisfy the law of the allometric growth, i.e., [Image: see text]. We construct clickstream networks and explain the observed temporal dynamics of networks by the interactions between nodes. We describe the transportation of clickstreams using the function [Image: see text], in which [Image: see text] is the total amount of clickstreams passing through node [Image: see text] and [Image: see text] is the amount of the clickstreams dissipated from [Image: see text] to the environment. It turns out that [Image: see text], an indicator for the efficiency of network dissipation, not only negatively correlates with [Image: see text], but also sets the bounds for [Image: see text]. In particular, [Image: see text] when [Image: see text] and [Image: see text] when [Image: see text]. Our findings have practical consequences. For example, [Image: see text] can be used as a measure of the “stickiness” of forums, which quantifies the stable ability of forums to remain users “lock-in” on the forum. Meanwhile, the correlation between [Image: see text] and [Image: see text] provides a method to predict the long-term “stickiness” of forums from the clickstream data in a short time period. Finally, we discuss a random walk model that replicates both of the allometric growth [Image: see text] and the dissipation function [Image: see text].