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The investigations of financial markets from a complex network perspectivehave unveiled many phenomenological properties, in which the majority of thesestudies map the financial markets into one complex network. In this work, weinvestigate 30 world stock market indices through their visibility graphs byadopting the visibility algorithm to convert each single stock index into onevisibility graph. A universal allometric scaling law is uncovered in theminimal spanning trees, whose scaling exponent is independent of the stockmarket and the length of the stock index. In contrast, the maximal spanningtrees and the random spanning trees do not exhibit universal allometric scalingbehaviors. There are marked discrepancies in the allometric scaling behaviorsbetween the stock indices and the Brownian motions. Using surrogate timeseries, we find that these discrepancies are caused by the fat-tailedness ofthe return distribution, the nonlinear long-term correlation, and a couplingeffect between these two influence factors.

Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices