The Metabolism and Growth of Web Forums

We view web forums as virtual living organisms feeding on user's attention and investigate how these organisms grow at the expense of collective attention. We find that the "body mass" ($PV$) and "energy consumption" ($UV$) of the studied forums exhibits the allometric growth property, i.e., $PV_t \sim UV_t ^ \theta$. This implies that within a forum, the network transporting attention flow between threads has a structure invariant of time, despite of the continuously changing of the nodes (threads) and edges (clickstreams). The observed time-invariant topology allows us to explain the dynamics of networks by the behavior of threads. In particular, we describe the clickstream dissipation on threads using the function $D_i \sim T_i ^ \gamma$, in which $T_i$ is the clickstreams to node $i$ and $D_i$ is the clickstream dissipated from $i$. It turns out that $\gamma$, an indicator for dissipation efficiency, is negatively correlated with $\theta$ and $1/\gamma$ sets the lower boundary for $\theta$. Our findings have practical consequences. For example, $\theta$ can be used as a measure of the "stickiness" of forums, because it quantifies the stable ability of forums to convert $UV$ into $PV$, i.e., to remain users "lock-in" the forum. Meanwhile, the correlation between $\gamma$ and $\theta$ provides a convenient method to evaluate the `stickiness" of forums. Finally, we discuss an optimized "body mass" of forums at around $10^5$ that minimizes $\gamma$ and maximizes $\theta$.