  In this paper, we define a stochastic Sierpinski gasket, on the basis of
which we construct a network called random Sierpinski network (RSN). We
investigate analytically or numerically the statistical characteristics of RSN.
The obtained results reveal that the properties of RSN is particularly rich, it
is simultaneously scale-free, small-world, uncorrelated, modular, and maximal
planar. All obtained analytical predictions are successfully contrasted with
extensive numerical simulations. Our network representation method could be
applied to study the complexity of some real systems in biological and
information fields.
