A Deterministic Box-covering Algorithm for Fractal Dimension Calculation of Complex Networks

Calculating the fractal dimension of complex networks by using a box-covering algorithm has attracted tremendous attention. However, the existing methods have randomness characteristics and depend on heavy computational bandwidth. To address these issues, deterministic box-covering algorithm is proposed for the calculation of fractal dimension in this paper. Firstly, the weight of each edge is obtained by the multiplication of degrees of the two connected nodes, and nodes are colored in order of degree from large to small. Furthermore, the sequence of nodes with the same degree is rearranged to get the minimum number of boxes. The Lastly, the fractal dimensions of a theoretical scale-free network and three real networks are investigated by the deterministic box-covering algorithm. All these results demonstrate that deterministic box-covering algorithm is serviceable in fractal dimension calculation of complex networks with high accuracy and less calculation.