Unveiling the Multi-fractal Structure of Complex Networks
arXiv:1610.06662 · doi:10.1016/j.chaos.2017.01.021
Abstract
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding method for revealing changes in the fractal behavior of networks, and particularly for allowing distinction between mono-fractal, quasi mono-fractal, and multi-fractal structures. We show that degree homogeneity plays a crucial role in determining the fractal nature of the underlying network, and report on six different protein-protein interaction networks along with their corresponding random networks. Our analysis allows to identify varying levels of complexity in the species.
arXiv comment7 pages, 4 figures, and 9 pages Supplementary Material
References in corpus (7)
- Self-similarity of complex networks
- How to calculate the fractal dimension of a complex network: the box covering algorithm
- A Geometric Fractal Growth Model for Scale Free Networks
- The Large-Scale Smoothness of the Universe
- Fractality in complex networks: critical and supercritical skeletons
- Multifractal Network Generator
- Quantifying randomness in protein-protein interaction networks of different species: A random matrix approach