A time-based complex network analysis on the seismic activity along the coast of Chile was made. The coast of Chile was divided on windows of 300 km in Latitude, from Arica up to Los Angeles. The window was moved 100 km from north to south. We built a time-based earthquake complex network, on each window and we studied a directed and undirected complex network. Assuming a self-similar data network, for the directed network we found the value of the power-law characteristic exponent γ for the connectivity probability distribution. For the directed network, we analyzed the average path length, measured through steps and meters, of the data set. For each window, we obtained a similar relation between the value of γ and the average path length. The exponents and values were evaluated for the data set with the total number of seismic events with a depth greater than 200 km and of magnitude greater than Mw=3.0.