Unveiling the multi-fractal structure of complex networks. (April 2017) - Jalan, Sarika; Yadav, Alok; Sarkar, Camellia; Boccaletti, Stefano
Highlights: A novel method of measurement of fractal dimension is proposed. The method uses graphs edges as basic unit in contrast to traditional methods. Our analysis allows identifying varying levels of complexity in the species. Abstract: The fractal nature of graphs has traditionally been investigated by using the network's nodes as the basic units. Here, instead, we propose to concentrate on the graph's 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.