Scale-free and small-world properties of a multiple-hub network with fractal structure

In this paper, we introduce a new kind of multiple-hub network with fractal structure. We aim to present a study on some properties of this network, such as the box dimension of the adjacency matrix, degree distribution, average clustering coefficient and average path length, which show the scale-free and small-world effects of this network. •Study a multiple-hub network with fractal structure.•Apply a renormalization group transformation to this network.•Calculate the box dimension of the adjacency matrix and the degree distribution.•Calculate the average clustering coefficient and the average path length.•This network has scale-free and small-world effects.