Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation

Abstract

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.

6 pages, 5 figures, accepted by EPL

References in corpus (2)

• Recursive graphs with small-world scale-free properties
• Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices

Cited by in corpus (13)

• Exact solution for mean first-passage time on a pseudofractal scale-free web
• Random Sierpinski network with scale-free small-world and modular structure
• Small-World Bonds and Patchy Percolation on the Hanoi Network
• Evolving small-world scale-free networks consist of cliques
• Mean first-passage time for random walks on the T-graph
• Average distance in a hierarchical scale-free network: an exact solution
• Topologies and Laplacian spectra of a deterministic uniform recursive tree
• Recursive solutions for Laplacian spectra and eigenvectors of a class of growing treelike networks
• Effects of accelerating growth on the evolution of weighted complex networks
• A geometric growth model interpolating between regular and small-world networks
• Geometry and Dynamics for Hierarchical Regular Networks
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• The rigorous solution for the average distance of a Sierpinski network