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

Chaoming Song, Lazaros K. Gallos, Shlomo Havlin, Hernán A. Makse

Research output: Contribution to journalArticle

199 Scopus citations

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 colouring 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 algorithms presented 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 one-week trip to our lab in New York (details in http://jamlab.org).

Original languageEnglish (US)
Article numberP03006
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number3
DOIs
StatePublished - Mar 1 2007
Externally publishedYes

Keywords

  • Analysis of algorithms
  • Growth processes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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