# Algorithm for Calculating the Fractal Dimension of Internet AS-Level Topology

• Jun Zhang
• Hai Zhao
• Wenbo Qi
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 849)

## Abstract

A box-covering algorithm to calculate the fractal dimension of Internet topology at AS-level was introduced. The algorithm first selects some nodes that have big degree and put them into different boxes, and then uses the node as seed in each box to cover the network. The purpose is to ensure that the boxes to cover the network are as little as possible. By analyzing a large number of the actual measurement data of AS-level topology, we found the relationship between the number of the nodes that were first selected as seeds and the size of the network. The number of the boxes to cover the network obtained by this algorithm is very close to the minimum number of boxes needed to cover the entire network. The results show that the algorithm can get the near-optimal solutions to cover the Internet network at AS-level without an exhaustive search, and thus effectively saves the time for calculating the fractal dimension of Internet topology at AS-level.

## Keywords

Complex network Box-Covering Fractal dimension AS-Level topology

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