Beyond traditional box-covering: Determining the fractal dimension of complex networks using a fixed number of boxes of flexible diameter

Abstract: In this paper, we present a novel box-covering algorithm for analyzing the fractal properties of complex networks. Unlike traditional algorithms that impose a predefined box size, our approach assigns nodes to boxes identified by the nearest local hubs without rigid distance constraints. This flexibility directly relates to the recently proposed scaling theory of fractal complex networks and is clearly consistent with the idea of hidden metric spaces in which network nodes are embedded. It also allows us to determine the box dimension of various real and model-based complex networks more accurately, including those previously unrecognized as fractal, such as the Internet at the level of autonomous systems. We show that our algorithm not only significantly reduces computational complexity compared to the classical greedy coloring method but also enables more precise determination of various scaling exponents describing the structure of fractal networks.