  Fractional Brownian motion (fBm) has been used as a theoretical framework to
study real time series appearing in diverse scientific fields. Because its
intrinsic non-stationarity and long range dependence, its characterization via
the Hurst parameter H requires sophisticated techniques that often yield
ambiguous results. In this work we show that fBm series map into a scale free
visibility graph whose degree distribution is a function of H. Concretely, it
is shown that the exponent of the power law degree distribution depends
linearly on H. This also applies to fractional Gaussian noises (fGn) and
generic f^(-b) noises. Taking advantage of these facts, we propose a brand new
methodology to quantify long range dependence in these series. Its reliability
is confirmed with extensive numerical simulations and analytical developments.
Finally, we illustrate this method quantifying the persistent behavior of human
gait dynamics.
