Most algorithms proposed for solving complex problems require the definition of some parameter values. The process of finding suitable parameter values is an optimization problem by itself. Understanding the global structure of search spaces of complex optimization problems remains a challenge. Moreover, understanding the relationship between parameter values and the performance of metaheuristics is a key issue on their development. Local optima networks propose a scheme to model search spaces as networks whose nodes represent local optima and edges represent transitions between them. In this work, we adapt the local optima network model to analyze and visualize the global structure of parameter configuration spaces. Our main objectives are to understand the structure of these networks and explore the difficulty of different tuning scenarios using common indicators previously proposed in local optima networks studies (e.g. number of local optima, number of global optima and presence of local and global funnels). For this, we use the well-known tuning method ParamILS to analyze configuration search spaces of a standard genetic algorithm that solves continuous optimization problems.