How to calculate the fractal dimension of a complex network: the box covering algorithm

Covering a network with the minimum possible number of boxes can reveal interesting features for the network structure, especially in terms of self-similar or fractal characteristics. Considerable attention has been recently devoted to this problem, with the finding that many real networks are self-similar fractals. Here we present, compare and study in detail a number of algorithms that we have used in previous papers towards this goal. We show that this problem can be mapped to the well-known graph coloring problem and then we simply can apply well-established algorithms. This seems to be the most efficient method, but we also present two other algorithms based on burning which provide a number of other benefits. We argue that the presented algorithms provide a solution close to optimal and that another algorithm that can significantly improve this result in an efficient way does not exist. We offer to anyone that finds such a method to cover his/her expenses for a 1-week trip to our lab in New York (details in http://jamlab.org).