Networks don't have to be electronic -- some early attempts at the telegraph involved making bubbles of different sizes float up in a water tank. A network is, basically, any means of transmitting information. A group of people talking to one another is broadcasting information wirelessly (sound) to multiple nodes (listeners), who process the information and translate it to actions or responses.
At the bottom level, computers are powered by diodes, which are tiny relays, mechanically actuated by tiny flows of electric current. One diode is hardly a network, and two diodes is like two mechanical switches -- and every mechanical switch transmits information in the same way that a diode does, by being either on or off.
So, for example, if a car has AC, headlights, and an engine, then that's three subsystems requiring at least three bits of information to run (three mechanical switches); and if the key has any complexity at all then it also requires several switches inside it. When turning on the engine, several other parts of the car also activate: power steering, breaks, whatever; that's one switch sending multiple "on"-signals. Every one of these signals is a bit (or multiple bits) of information.
Your society will have to answer three basic questions:
- How much information counts as "networked information" -- how many "on/off" relationships can one device send/receive with another device?
- How many devices may communicate with one another by means of these signals at one time, without direct human intervention?
- How many moving parts counts as "one device" for the purpose of determining communication between devices?
If the answer to #1 is "1 bit", then you could reasonably use any mechanical switch, but you can't do any logical functions (like a "j/k flip-flop"), so you can't have a house where two light-switches change the state of the same lightbulb.
If the answer to #2 is "2 devices", then you might have to flip 3 to 5 switches to get your car started.
If the answer to #3 is "one moving part", and #1 and #2 are "1 bit" and "2 devices", then your door-locks are limited to skeleton keys with only 2 stages, because one turn of the key can only actuate two devices, and each device is defined as one moving part (one tumbler), and each tumbler may only perform one action on the bolt. This is an extreme example, but I'm trying to establish consistency across technologies.
Another one: imagine a person presses a button which links a large battery to ground, through a coil, generating a magnetic signal. Across the room, an RLC circuit picks up the field, opens a diode through a local source of electricity, and powers another coil which drives a piston across your window, drawing the curtains. If each electric device counts as a small moving part, you have arguably six moving parts on one 1-bit signal:
- RLC circuit (minimum 2 devices excluding resistors: L and C)
That can be construed as:
- 1 human interaction, 1 device (6 moving parts), 1 bit of information being transmitted once from human-to-device
- 1 human interaction, 2 devices (one with 2 moving parts, the other with 4 moving parts), one bit being transmitted once from human-to-device, and once device-to-device.
- 1 human interaction, 6 devices (1 moving part each), one bit being transmitted once from human-to-device, and 5 times device-to-device.
So, that setup would be allowable if they said "one device has 6 moving parts, and only one device may actuate per human interaction", or if they said, "one device has only one moving part, and 6 devices can communicate with one another per human interaction".
Once you've got the rules defined, then each piece of technology will have to be reworked according to those rules.