This paper introduces the *visibility algorithm*, a computational method that converts time series into graphs. The constructed graph retains key properties of the original series, such as periodicity, randomness, and fractality. Periodic series are mapped into regular graphs, random series into random graphs, and fractal series into scale-free networks. The algorithm is formally defined, ensuring the graph is connected, undirected, and invariant under affine transformations. The method is compared with another mapping technique by Zhang and Small, highlighting differences in applicability and graph connectivity. The paper explores the degree distribution of the visibility graph for various series, showing that it reflects the underlying structure of the time series. For fractal series, the degree distribution follows a power law, and the network exhibits either a Small-World effect or scale invariance, depending on the series type. The visibility algorithm provides a new tool for characterizing time series using complex network theory, with potential applications in estimating Hurst exponents and detecting inverse bifurcations in chaotic systems.This paper introduces the *visibility algorithm*, a computational method that converts time series into graphs. The constructed graph retains key properties of the original series, such as periodicity, randomness, and fractality. Periodic series are mapped into regular graphs, random series into random graphs, and fractal series into scale-free networks. The algorithm is formally defined, ensuring the graph is connected, undirected, and invariant under affine transformations. The method is compared with another mapping technique by Zhang and Small, highlighting differences in applicability and graph connectivity. The paper explores the degree distribution of the visibility graph for various series, showing that it reflects the underlying structure of the time series. For fractal series, the degree distribution follows a power law, and the network exhibits either a Small-World effect or scale invariance, depending on the series type. The visibility algorithm provides a new tool for characterizing time series using complex network theory, with potential applications in estimating Hurst exponents and detecting inverse bifurcations in chaotic systems.