The visibility graph method converts time series into graphs, preserving key properties of the original data. This method maps a time series into a network where nodes represent data points and edges represent visibility between points. Periodic series generate regular graphs, random series generate random graphs, and fractal series generate scale-free networks. The visibility graph inherits structural properties of the time series, enabling the characterization of complex dynamics. The visibility algorithm defines visibility between two points based on a criterion that ensures no intermediate data point blocks the line of sight. This results in a graph that is always connected, undirected, and invariant under affine transformations. The method is compared to other approaches, such as those by Zhang and Small, highlighting differences in applicability and graph structure. For periodic series, the visibility graph is regular, with degree distributions reflecting the series' period. For random series, the degree distribution is exponential, indicating the presence of hubs. Fractal series produce scale-free networks, with degree distributions following power laws, demonstrating the relationship between fractality and scale-free properties. The visibility graph of Brownian motion exhibits a Small-World effect, while the Conway series shows self-similarity. The method can distinguish between different types of fractality, as demonstrated by the degree distribution of nodes in fractal series. The visibility graph also captures hub repulsion, a characteristic of fractal networks. The method is robust and can be generalized to weighted networks for quantitative analysis. It has applications in estimating Hurst exponents and analyzing chaotic systems. The visibility graph provides a bridge between time series analysis and complex network theory, enabling the characterization of non-trivial time series and offering insights into fractal structures.The visibility graph method converts time series into graphs, preserving key properties of the original data. This method maps a time series into a network where nodes represent data points and edges represent visibility between points. Periodic series generate regular graphs, random series generate random graphs, and fractal series generate scale-free networks. The visibility graph inherits structural properties of the time series, enabling the characterization of complex dynamics. The visibility algorithm defines visibility between two points based on a criterion that ensures no intermediate data point blocks the line of sight. This results in a graph that is always connected, undirected, and invariant under affine transformations. The method is compared to other approaches, such as those by Zhang and Small, highlighting differences in applicability and graph structure. For periodic series, the visibility graph is regular, with degree distributions reflecting the series' period. For random series, the degree distribution is exponential, indicating the presence of hubs. Fractal series produce scale-free networks, with degree distributions following power laws, demonstrating the relationship between fractality and scale-free properties. The visibility graph of Brownian motion exhibits a Small-World effect, while the Conway series shows self-similarity. The method can distinguish between different types of fractality, as demonstrated by the degree distribution of nodes in fractal series. The visibility graph also captures hub repulsion, a characteristic of fractal networks. The method is robust and can be generalized to weighted networks for quantitative analysis. It has applications in estimating Hurst exponents and analyzing chaotic systems. The visibility graph provides a bridge between time series analysis and complex network theory, enabling the characterization of non-trivial time series and offering insights into fractal structures.