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We analyze the properties of the majority-vote (MV) model with an additional noise in which a local spin can be changed independently of its neighborhood. In the standard MV, one of the simplest nonequilibrium systems exhibiting an order–disorder phase transition, spins are aligned with their local majority with probability 1− f, and with complementary probability f, the majority rule is not followed. In the noisy MV (NMV), a random spin flip is succeeded with probability p (with complementary 1− p the usual MV rule is accomplished). Such extra ingredient was considered by Vieira and Crokidakis (2016) for the square lattice. Here, we generalize the NMV for arbitrary networks, including homogeneous [random regular (RR) and Erdös–Renyi (ER)] and heterogeneous [Barabasi–Albert (BA)] structures, through mean-field calculations and numerical simulations. Results coming from both approaches are in excellent …