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How to calculate the fractal dimension of a complex network: the box covering algorithm | | Chaoming Song
; Lazaros K. Gallos
; Shlomo Havlin
; Hernan A. Makse
; | | Date: |
10 Jan 2007 | | Subject: | Disordered Systems and Neural Networks; Statistical Mechanics | | Abstract: | 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 this http URL). | | Source: | arXiv, cond-mat/0701216 | | Services: | Forum | Review | PDF | Favorites | |
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