The Network Interface Card (NIC) or modem (Dial-up) controls the flow of data between your computer and the cable.
Peer to Peer Network ... as i think ...
Strictly speaking, no computer 'controls' a network. You will have different devices that do different jobs on a network. Some examples : You might have a DOMAIN CONTROLLER on a Microsoft network...
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There is no such thing as a 'default network'. Perhaps you meant 'default gateway'?