Core-periphery disparity in fractal behavior of complex networks

We show that there is a disparity in fractal scaling behavior of the core and peripheral parts of empirical small-world scale-free networks. We decompose the network into a core and a periphery and measure the fractal dimension of each part separately using the box-counting method. We find that the core of small-world scale-free networks has a nonfractal structure, whereas the periphery exhibits either fractal or nonfractal scaling. The fractal dimension of the periphery is found to coincide with one for the whole network.