The neuropathology of schizophrenia remains unclear. Some insight has come from modern neuroimaging techniques, which offer an unparalleled opportunity to explore in vivo the structure and function of the brain. Using functional magnetic resonance imaging, it has been found that the large-scale resting-state functional connectivity (rsFC) in schizophrenia - measured as the temporal correlations of the blood-oxygen-level-dependent (BOLD) signal - exhibit altered network topology, with lower small-world index. The origin of these rsFC alterations and link with the underlying structural connectivity remain unclear. In this work, we used a computational model of spontaneous large-scale brain activity to explore the role of the structural connectivity in the large-scale dynamics of the brain in health and schizophrenia. The structural connectomes from 15 adolescent patients with early-onset schizophrenia and 15 age- and gender-matched controls were built from diffusion tensor imaging data to detect the white matter tracts between 90 brain areas. Brain areas, simulated using a reduced dynamic mean-field model, receive excitatory input from other areas in proportion to the number of fibre tracts between them. The simulated mean field activity was transformed into BOLD signal, and the properties of the simulated functional networks were analyzed. Our results suggest that the functional alterations observed in schizophrenia are not directly linked to alterations in the structural topology. Instead, subtly randomized and less small-world functional networks appear when the brain operates with lower global coupling, which shifts the dynamics from the optimal healthy regime.