Abstract
Research on fractal networks is a dynamically growing field of network science. A central issue is to analyze the fractality with the so-called box-covering method. As this problem is known to be NP-hard, a plethora of approximating algorithms have been proposed throughout the years. This study aims to establish a unified framework for comparing approximating box-covering algorithms by collecting, implementing, and evaluating these methods in various aspects including running time and approximation ability. This work might also serve as a reference for both researchers and practitioners, allowing fast selection from a rich collection of box-covering algorithms with a publicly available codebase.
Highlights
It is a challenging task to develop notions that can capture important features of a realworld network
The difference between the two conventions might seem very minor and some authors argue that the particular definition has no effect on the fractal scaling, Rosenberg (2020) emphasizes that it can make a large difference
Preliminaries Here we describe the boxing process we applied in our experiments
Summary
It is a challenging task to develop notions that can capture important features of a realworld network. Various classes of networks, such as small-world networks, scale-free networks, and networks with a strong community structure have attracted a lot of research attention in the past two decades (Molontay and Nagy 2021). There has been an increasing interest in the class of fractal networks, since fractality has been verified in several real-world networks (WWW, actor collaboration networks, protein interaction networks) (Song et al 2005; Wen and Cheong 2021). Fractality has been associated with many important properties of networks such as robustness, modularity, and information contagion (Rozenfeld et al 2007). For a wide range of applications of fractal property in networks, see the work of Wen and Cheong (2021)
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