With the huge amount of data that has been collected over time, many methods are being developed to allow better understanding and forecasting in several domains. Time series analysis is a powerful tool to achieve this goal. Despite being a well-established area, there are some gaps, and new methods are emerging to overcome these limitations, such as visibility graphs. Visibility graphs allow the analyses of times series as complex networks and make possible the use of more advanced techniques from another well-established area, network science. In this paper, we present two new efficient approaches for computing natural visibility graphs from times series, one for online scenarios in \(\mathcal {O}(n\log {n})\) and the other for offline scenarios in \(\mathcal {O}(nm)\) , the latter taking advantage of the number of different values in the time series (m).