Networked communications are arguably the foundation of the movie. Without this form of communication, "hitchhiking" would not be possible. There are several examples of networked communications throughout the movie.
Examples From the Movie
The first example we see is the sub-etha Sens-O-Matic. This device is used along with the signaling device to alert hitchhikers about nearby spacecrafts. The sub-etha signal is a faster-than-light communication network widely used throughout the universe.
Similar to the Sens-O-Matic device this device, also referred to as the "electronic thumb," is worn as a ring by Ford throughout the movie which allows hitchhikers to flag down passing spacecraft to hitch a lift (1).
In order to communicate between the spaceships, video calls are made between the spacecraft (2).
When pointed at a person and the trigger is pulled, the target automatically sees things from your point of view. This is arguably networked communication because the target can see your perspective through technology.
Sources
https://www.usenix.org/legacy/publications/library/proceedings/lisa93/full_papers/evard.pdf
Image Sources in Order Presented