  We use advanced statistical tools of time-series analysis to characterize the
dynamical complexity of the transition to optical wave turbulence in a fibre
laser. Ordinal analysis and the horizontal visibility graph applied to the
experimentally measured laser output intensity reveal the presence of temporal
correlations during the transition from the laminar to the turbulent lasing
regimes. Both methods unveil coherent structures with well defined time-scales
and strong correlations both, in the timing of the laser pulses and in their
peak intensities. Our approach is generic and may be used in other complex
systems that undergo similar transitions involving the generation of extreme
fluctuations.
