We propose a parallel resistance model (PRM) in which total resistance (Rtotal) is given by the parallel connection of resistance of a filament (Rfila) and that of a film excluding the filament (Rexcl)—that is, 1/Rtotal = 1/Rfila + 1/Rexcl—to understand direct current (dc) electric properties of resistive random-access memory (ReRAM). To prove the validity of this model, the dependence of the resistance on temperature, R(T), and the relative standard deviation (RSD) of RHRS of Pt/NiO/Pt on the area of a top electrode, S, are investigated. It is clarified that both the R(T) and RSD depended on S, and all such dependencies can be explained by the PRM. The fact that Rtotal is decided by the magnitude relation between Rfila and Rexcl makes transport properties S-dependent and hinders the correct understanding of ReRAM. Smaller S is essential to observe the intrinsic transport properties of ReRAM filaments.