Velocity time series of hydrodynamic and magnetohydrodynamic (MHD) turbulent flow are analyzed by means of complex network analysis in order to understand the mechanism of fluid patterns modification due to the external magnetic field. Direct numerical simulations of two cases are used, one for the plane hydrodynamic turbulent channel flow at the low Reynolds number of 180, based on the friction velocity, and the corresponding MHD flow with an external streamwise magnetic field with a magnetic interaction number of 0.1. By applying the visibility graph algorithm, we first transformed the time series into networks and then we evaluated the network topological properties. Results show that the proposed network analysis is not only able to identify and detect dynamical transitions in the system's behavior that identifies three distinct fluid areas in accordance with turbulent flow theory but also can quantify the effect of the magnetic field on the time series transitions. Moreover, we find that the topological measures of networks without a magnetic field and as compared to the one with a magnetic field are statistically different within a 95% confidence interval. These results provide a way to discriminate and characterize the influence of the magnetic field on the turbulent flows.