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The dynamics of a complex system is usually recorded in the form of timeseries, which can be studied through its visibility graph from a complexnetwork perspective. We investigate the visibility graphs extracted fromfractional Brownian motions and multifractal random walks, and find that thedegree distributions exhibit power-law behaviors, in which the power-lawexponent $\alpha$ is a linear function of the Hurst index $H$ of the timeseries. We also find that the degree distribution of the visibility graph ismainly determined by the temporal correlation of the original time series withminor influence from the possible multifractal nature. As an example, we studythe visibility graphs constructed from two Chinese stock market indexes andunveil that the degree distributions have power-law tails, where the tailexponents of the visibility graphs and the Hurst indexes of the indexes areclose to the $\alpha\sim H$ linear relationship.

Degree distribution of the visibility graphs mapped from fractional Brownian motions and multifractal random walks