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This study investigates the effects generated by tourism events and investments to improve destination development (dynamics) and stability (topology). The horizontal visibility graph framework (a technique able to transform a time series into a network) was used. Two hypotheses were tested: the first was the ability of these events and investments to generate a turning point, and the second was their ability to increase the system’s stability. The findings are based on a longitudinal analysis of three different destinations in terms of size, type of destination events and investments, and the prevalent market segment. For each case, a daily longitudinal time series was considered, and the empirical evidence confirmed both hypotheses. In the concluding remarks, the theoretical and empirical implications are reported, and some future research avenues are discussed.