As the memristor device is asymmetrical in nature, it is not a bilateral element like the resistor in terms of circuit functionality. Thus, it causes hindrance in some memristor-based applications such as in cellular nonlinear network neighborhood connections and in some application areas where its orientation is essentially expected to act as a bilateral circuit element reliable for bidirectional communication, for example, in signal and image processing or in electrical synapse devices. We introduce a memristor-based network for each purpose where we replace the conventional series resistances by memristors. The memristor asymmetry is described from the circuit point of view allowing us to observe its interaction within the network. Moreover, a memristor fuse is proposed in order to achieve the memristive effect with symmetry, which is formed basically by connecting two memristors antiserially. We, therefore, analyze the memristor fuse from its basic principle along with the theoretical analysis and then observe the response from the circuit point of view.