This paper presents the results of a sensitivity analysis of the characteristics of discrete fracture network (DFN) connectivity. The sizes of the maximum and mean clusters comprising the DFN and the distribution of the connectivity index were estimated. Attention was primarily directed to the global sensitivity analysis of these characteristics. Sobol sensitivity indices were used to determine the relative contribution of the DFN model parameter uncertainty to the total uncertainty of the studied problem. Dominant Sobol indices for different DFN models and each fracture connectivity characteristic were determined. The analysis of the results allowed the identification of the parameters whose relevant probability distributions are most important for the correct description of the studied statistical model.