What does “rules and protocols for communication across the network” mean in GPLv3?
This refers to rules about traffic you can send over the network. For example, if there is a limit on the number of requests you can send to a server per day, or the size of a file you can upload somewhere, your access to those resources may be denied if you do not respect those limits. These rules do not include anything that does not pertain directly to data traveling across the network. For instance, if a server on the network sent messages for users to your device, your access to the network could not be denied merely because you modified the software so that it did not display the messages.
