Optimal box-covering algorithm for fractal dimension of complex networks

TL;DR

This paper presents a new box-covering algorithm that efficiently finds optimal solutions for analyzing the self-similarity of complex networks, demonstrating significant improvements over previous methods.

Contribution

The introduced algorithm outperforms existing methods and guarantees optimal solutions for fractal dimension analysis of complex networks.

Findings

Up to 15% improvement in box-covering efficiency for WWW network

Achieves optimal solutions in benchmark tests

Enhances understanding of network self-similarity

Abstract

The self-similarity of complex networks is typically investigated through computational algorithms the primary task of which is to cover the structure with a minimal number of boxes. Here we introduce a box-covering algorithm that not only outperforms previous ones, but also finds optimal solutions. For the two benchmark cases tested, namely, the E. Coli and the WWW networks, our results show that the improvement can be rather substantial, reaching up to 15% in the case of the WWW network.