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Signals from heart transplant recipients can be considered to be a natural source of information for a better understanding of the impact of the autonomic nervous system on the complexity of heart rate variability. Beat-to-beat heart rate variability can be represented as a network of increments between subsequent $RR$-intervals, which makes possible the visualization of short-term heart period fluctuations. A network is constructed of vertices representing increments between subsequent $RR$-intervals, and edges which connect adjacent $RR$-increments. Two modes of visualization of such a network are proposed. The method described is applied to nocturnal Holter signals recorded from healthy young people and from cardiac transplant recipients. Additionally, the analysis is performed on surrogate data: shuffled RR-intervals (to display short-range dependence), and shuffled phases of the Fourier Transform of RR-intervals (to filter out linear dependences). Important nonlinear properties of autonomic nocturnal regulation in short-term variability in healthy young persons are associated with $RR$-increments: accelerations and decelerations of a size greater than about 35 ms. They reveal that large accelerations are more likely antipersistent, while large decelerations are more likely persistent. Changes in $RR$-increments in a heart deprived of autonomic supervision are much lower than in a healthy individual, and appear to be maintained around a homeostatic state, but there are indications that this dynamics is nonlinear. The method is fruitful in the evaluation of the vagal activity - the quantity and quality of the vagal tone - during the nocturnal rest of healthy young people. The method also successfully extracts nonlinear effects related to intrinsic mechanisms of the heart regulation., Comment: 20 pages, 7 figures. Article submitted as a chapter in the book 'Interpretation of ECG time series using inter-beat variability analysis: From engineering to medicine' ed. by H. Jelinek