The effect of sulfur/accelerator amount (at fixed ratio) and accelerator type (n-cyclohexyl-benzothiazole-2-sulfenimide, diphenylguanidine) on network parameters (network chain density, cross-linking density, tube diameter, trapping factor) of styrene-butadiene copolymer networks is investigated via uniaxial stress-strain measurements up to large extensions. The mechanical properties are discussed in the framework of a non-Gaussian network model. It includes topological constraints for the network chains and the network junctions (cross-links and trapped entanglements). The model assumes a trapped entanglement contribution to the stress that does not vanish in the infinite strain limit. The two types of junctions (cross-links and trapped entanglements) are assumed to fluctuate in a Flory-Kastner domain around their mean position, while the chain segments fluctuate in a conformational tube built up by the surrounding chains. The finite extensibility component of the measured stress is evaluated by using a series expansion of the inverse Langevin function. The typical network parameters are estimated from the Gaussian contribution to the stress. It is found that the cross-link contribution G(c) of the moduli changes approximately linearly with the concentration of cross-linking agent sulfur. Vanishing values of the moduli G(c) are found at finite concentrations of cross-linking agent that are related to the gel point. The concentrations of cross-links at the gel points are almost identical for both systems of accelerators whereas the estimated cross-linking efficiencies are different. In relation to the estimated structure parameters, some measured technically important mechanical properties (tensile strength, hardness, rebound resilience, dynamic losses) of the differently accelerated sulfur-cured SBR networks are discussed qualitatively in the framework of the proposed network model.