A statistically conceptualized fracture network is generally used in modeling flow and transport in the discrete fracture network (DFN) approach. To quantify the influence of the fracture connectivity and characterization level on the uncertainty from a statistical conceptualization of fractures, the ensemble mean and variability of the equivalent permeability for stochastically generated fracture networks is analyzed with various percolation parameters (p) for different structures following power law size distributions. The results of Monte Carlo analyses show that statistics of a fracture network can be used to estimate its hydraulic properties with an acceptable level of uncertainty when p is greater than the specific percolation parameter (p (s)) where the domain size is expected to become equal to the correlation length of a given fracture network. However, when p is smaller than the p (s), the uncertainty of the hydraulic properties induced from statistical characteristics of fractures is large, thus statistical conceptualization is not recommended. Conditional simulations support them: although we have deterministic information on a significant amount of fractures in the domain, a small number of stochastically generated fractures still produce significant uncertainty in the estimated system properties when p is smaller than p (s). These results suggest that the p (s) and correlation length of a fracture network can be criteria to evaluate the applicability of the statistical conceptualization for modeling flow in a given fractured rock.