Will a 100 Mbit/s wired router slow down my internal network speeds? (See diagram)

Solution 1:

Your internal network will not be any slower due to the fact that all devices will communicate to each other directly (by ARPing and storing MAC addresses). You will be a little slower when you interface with the router (web administration, etc.), but that should not be noticeable.

Traffic going through the router (such as going to the Internet) will be slower than your internal, but generally most consumer connections are not greater than 100 Mbit/s and as such your Internet traffic will be limited by that.

This answer assumes your gigabit hubs are in fact switches as those are more common.