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Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski networks, which are induced by the famous Sierpinski fractals and constructed in a simple iterative way. We derive analytical expressions for degree distribution, strength distribution, clustering coefficient, and strength-degree correlation, which agree well with the characterizations of various real-life networks. Moreover, we show that the introduced Sierpinski networks are maximal planar graphs.
We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the networks follo
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 reve
A vast variety of real-life networks display the ubiquitous presence of scale-free phenomenon and small-world effect, both of which play a significant role in the dynamical processes running on networks. Although various dynamical processes have been
Fractal scale-free networks are empirically known to exhibit disassortative degree mixing. It is, however, not obvious whether a negative degree correlation between nearest neighbor nodes makes a scale-free network fractal. Here we examine the possib
We investigate the accumulated wealth distribution by adopting evolutionary games taking place on scale-free networks. The system self-organizes to a critical Pareto distribution (1897) of wealth $P(m)sim m^{-(v+1)}$ with $1.6 < v <2.0$ (which is in