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In this paper, we define a stochastic Sierpinski gasket, on the basis ofwhich we construct a network called random Sierpinski network (RSN). Weinvestigate analytically or numerically the statistical characteristics of RSN.The obtained results reveal that the properties of RSN is particularly rich, itis simultaneously scale-free, small-world, uncorrelated, modular, and maximalplanar. All obtained analytical predictions are successfully contrasted withextensive numerical simulations. Our network representation method could beapplied to study the complexity of some real systems in biological andinformation fields.

Random Sierpinski network with scale-free small-world and modular structure