  We investigate the q-voter model with stochastic noise arising from
independence on complex networks. Using the pair approximation, we provide a
comprehensive, mathematical description of its behavior and derive a formula
for the critical point. The analytical results are validated by carrying out
Monte Carlo experiments. The pair approximation prediction exhibits substantial
agreement with simulations, especially for networks with weak clustering and
large average degree. Nonetheless, for the average degree close to q, some
discrepancies originate. It is the first time we are aware of that the
presented approach has been applied to the nonlinear voter dynamics with noise.
Up till now, the analytical results have been obtained only for a complete
graph. We show that in the limiting case the prediction of pair approximation
coincides with the known solution on a fully connected network.
