Critical infrastructure networks are continuously growing, gaining complexity with each urban sprawl, conurbation, technological change, and regulatory update. Consequently, their detailed risk analysis demands large amounts of data, computational resources (required by simulations, optimization, flow equilibria, etc.), and dealing with complex interpretations of the results. This comes with several drawbacks: scarcity of adequately curated data, which instead are usually incomplete and sometimes even incorrect, algorithmic runtime that impairs the full use of Monte Carlo simulations, errors that may propagate extensively, and results that cannot be generalized and extended to other cases. Therefore, researchers have also resorted to analyzing simplified versions of these infrastructure systems. This work evaluates three algorithms for reducing the complexity of infrastructure networks while keeping reasonable accuracy for statistical interpretation. These algorithms transform a detailed graph into a more compact representation, where risk assessments can be performed more easily. The strategies used herein are based on the detection of important edges (backbone detection) and the merging or lumping similar or proximate elements (clustering, contractions). The different complexity reduction algorithms are evaluated on three infrastructure networks, namely: the electric transmission network of Chile, the electric distribution network of the Greater Valparaíso and the drinking water distribution network of the Greater Valparaíso. The experiments show that two of the three graph reduction criteria proposed in this work yield good approximations of the connectivity of the original graphs, when these are reduced to 25% of their size.