  A new alternative method to approximate the Visibility Graph (VG) of a time
series has been introduced here. It exploits the fact that most of the nodes in
the resulting network are not connected to those that are far away from them.
This means that the adjacency matrix is almost empty, and its nonzero values
are close to the main diagonal. This new method is called Sliding Visibility
Graph (SVG). Numerical tests have been performed for several time series,
showing a time efficiency that scales linearly with the size of the series
[O(N)], in contrast to the original VG that does so quadratically [O(N2)]. This
fact is noticeably convenient when dealing with very large time series. The
results obtained from the SVG of the studied time series have been compared to
the exact values of the original VG. As expected, the SVG outcomes converge
very rapidly to the desired ones, especially for random and stochastic series.
Also, this method can be extended to the analysis of time series that evolve in
real time, since it does not require the entire dataset to perform the analysis
but a shorter segment of it. The length segment can remain constant, making
possible a simple analysis as the series evolves in time.
