  The majority-vote model with noise is one of the simplest nonequilibrium
statistical model that has been extensively studied in the context of complex
networks. However, the relationship between the critical noise where the
order-disorder phase transition takes place and the topology of the underlying
networks is still lacking. In the paper, we use the heterogeneous mean-field
theory to derive the rate equation for governing the model's dynamics that can
analytically determine the critical noise $f_c$ in the limit of infinite
network size $N\rightarrow \infty$. The result shows that $f_c$ depends on the
ratio of ${\left\langle k \right\rangle }$ to ${\left\langle k^{3/2}
\right\rangle }$, where ${\left\langle k \right\rangle }$ and ${\left\langle
k^{3/2} \right\rangle }$ are the average degree and the $3/2$ order moment of
degree distribution, respectively. Furthermore, we consider the finite size
effect where the stochastic fluctuation should be involved. To the end, we
derive the Langevin equation and obtain the potential of the corresponding
Fokker-Planck equation. This allows us to calculate the effective critical
noise $f_c(N)$ at which the susceptibility is maximal in finite size networks.
We find that the $f_c-f_c(N)$ decays with $N$ in a power-law way and vanishes
for $N\rightarrow \infty$. All the theoretical results are confirmed by
performing the extensive Monte Carlo simulations in random $k$-regular
networks, Erd\"os-R\'enyi random networks and scale-free networks.
