Epidemics are one of the most significant challenges throughout history, and climate change has contributed to the increasing frequency and diversity of outbreaks. It is the case of dengue fever, which has been responsible for hundreds of thousands of cases worldwide in the last decades. The proliferation of different serotypes and their association with other diseases have made the situation too complex, and there is an urgent demand for alternative approaches to fully understanding the dynamics of the outbreaks. In this work, we apply the visibility graph approach to analyze the time series of dengue occurrence patterns in two large Brazilian cities. We introduce a new impact-frequency histogram protocol to evaluate cyclic dengue patterns in a single plot. We analyzed the time series of cases and estimated a period for re-infestation of the disease. The tool has proven helpful in analyzing temporal series, especially for epidemic diseases.