Network: In general Network is the interconnection of various horizontal and vertical lines in a regular fashion.
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Electrical Network: (Logically speaking) It is the interconnection of all the electrical elements in a regular fashion to perform a specific tasks.
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Electrical Circuits: Moreover an electrical circuit is a network itself but it possess a closed path always, to make a circulation of currents inside the circuit.
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So, we can say that every circuit is a network but every network is not a circuit.