Disclaimer: This question was initially asked in Network Engineering SE, yet got closed due to its research nature.
Assume a (hypothetical) communications network constituted by many nodes including two adjacent nodes $u$ and $v$. Let the traffic at node $u$ (resp., node $v$), denoted by $f(u)$ (resp., $f(v)$), be the difference between number of packets entering $u$ (resp., $v$) and departing it during a particular time interval. For a particular simulation to show the validity of a complicated model, I need to assume that $f(u) = exp(f(v))$ and $f(v) = log(f(v))$, where $u$ and $v$ are generally connected to many other nodes, as well. I just searched a little bit in the literature but failed to find any real-world network in which such dynamics may hold. Since I am not a network expert, it is pretty likely that I have missed something. So, does anyone know such a network? Even if there is not a real network, I am curious whether one can imagine a reasonable network in which such exponential law is (at least locally) the case.
I have already read about power graphs of social networks that might be relevant to this question. However, I am strictly interested in a potential example in the realm of communications networks (computer networks, datacenter networks, ad-hoc networks, etc.).