Fractal and Transfractal Scale-Free Networks

Details Fractal and Transfractal Scale-Free Networks Fractal and Transfractal Scale-Free Networks

2008-08-16

arxiv.org/abs/0808.2206v1

Physics

Physics and Society

To appear in the Encyclopedia of Complexity and Systems Science

Scientific paper

Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century. The importance of fractal geometry stems from the fact that these structures were recognized in numerous examples in Nature, from the coexistence of liquid/gas at the critical point of evaporation of water, to snowflakes, to the tortuous coastline of the Norwegian fjords, to the behavior of many complex systems such as economic data, or the complex patterns of human agglomeration. Here we review the recent advances in self-similarity of complex networks and its relation to transport, diffusion, percolations and other topological properties such us degree distribution, modularity, and degree-degree correlations.

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