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 PV(t) (the number of page views in a given time period) and UV(t) (the number of unique visitors in the time period) of the studied forums satisfy the law of the allometric growth, i.e., PV(t) ~ UV(t)((θ). 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 D(i) ~ T(i)(γ), in which T(i) is the total amount of clickstreams passing through node i and D(i) is the amount of the clickstreams dissipated from i to the environment. It turns out that γ, an indicator for the efficiency of network dissipation, not only negatively correlates with θ, but also sets the bounds for θ. In particular, 1/γ > θ when 0 < γ < 1 and 1/γ < θ when γ > 1. Our findings have practical consequences. For example, θ 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 γ and θ 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 PV(t) ~ UV(t)(θ) and the dissipation function D(i) ~ T(γ)(i).