On the unique reconstruction of a signal from its unthresholded recurrence plot

► A recurrence plot determines at least the power spectrum of the underlying signal. ► Reconstructibility can be characterized in terms of the connectivity of a graph. ► If the graph is connected then the signal is determined up to a sign factor. ► We provide explicit expressions to reconstruct a signal and its power spectrum. ► We propose a distance measure for recurrence plots for approximation of signals.