The definition of fractal dimension of infinite growing sets is presented. It is based on a box-
counting approach and coincides with the elasticity coefficient for number of boxes as …

In this article, we introduce a new concept: the transfinite fractal dimension of graph
sequences motivated by the notion of fractality of complex networks proposed by Song et al …

Complex networks created by fractals have been associated with various applications such
as social networks, modern communication, and fractal antennas. In this paper, we consider …

For a family of networks {G n} n≥ 1, we define the Hausdorff dimension of {G n} n≥ 1
inspired by the Frostman's characteristics of potential for Hausdorff dimension of fractals on …

We discuss cluster growing method and box-covering method as well as their connection to
fractal geometry. Our measurements show that for small network systems, box-covering …

A random sequential box-covering algorithm recently introduced to measure the fractal
dimension in scale-free (SF) networks is investigated. The algorithm contains Monte Carlo …

In the field of network science, one of the fundamental questions is how to characterize a
network. One way to characterize a network is to compute a fractal dimension. We write “a …

We show that fractality in complex networks arises from the geometric self-similarity of their
built-in hierarchical community-like structure, which is mathematically described by the scale …

The concept of elasticity of graphs is presented. Elasticity factor is a scale-free measure of
graph density. Scale-free networks model with elasticity factor is proposed. Applying the …

We show that fractality in complex networks arises from the geometric self-similarity of their
built-in hierarchical community-like structure, which is mathematically described by the scale …