### 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 language | English (US) |
---|---|

Article number | P03006 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

- Analysis of algorithms
- Growth processes

### ASJC Scopus subject areas

- Statistics and Probability
- Statistical and Nonlinear Physics

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*, (3), [P03006]. https://doi.org/10.1088/1742-5468/2007/03/P03006

**How to calculate the fractal dimension of a complex network : The box covering algorithm.** / Song, Chaoming; Gallos, Lazaros K.; Havlin, Shlomo; Makse, Hernán A.

Research output: Contribution to journal › Article

*Journal of Statistical Mechanics: Theory and Experiment*, no. 3, P03006. https://doi.org/10.1088/1742-5468/2007/03/P03006

}

TY - JOUR

T1 - How to calculate the fractal dimension of a complex network

T2 - The box covering algorithm

AU - Song, Chaoming

AU - Gallos, Lazaros K.

AU - Havlin, Shlomo

AU - Makse, Hernán A.

PY - 2007/3/1

Y1 - 2007/3/1

N2 - 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).

AB - 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).

KW - Analysis of algorithms

KW - Growth processes

UR - http://www.scopus.com/inward/record.url?scp=42749104025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42749104025&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2007/03/P03006

DO - 10.1088/1742-5468/2007/03/P03006

M3 - Article

AN - SCOPUS:42749104025

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 3

M1 - P03006

ER -