Related papers: Graph fractal dimension and structure of fractal n…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
In this paper we introduce and study discrete analogues of Lebesgue and Hausdorff dimensions for graphs. It turned out that they are closely related to well-known graph characteristics such as rank dimension and Prague (or…
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-invariant equation for the masses of the boxes…
The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network…
Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century. The importance of fractal geometry stems from the fact that these structures were…
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
In this paper, we pose a hypothesis that the structure of communities in complex networks may result from their latent fractal properties. This hypothesis is based not only on the general observation that many real networks have multilevel…
In this work, we study the fractal and multifractal properties of a family of fractal networks introduced by Gallos {\it et al.} ({\it Proc. Natl. Acad. Sci. U.S.A.}, 2007, {\bf 104}: 7746). In this fractal network model, there is a…
Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In…
We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications.…
Recently [L. Lacasa and J. G\'omez-Garde\~nes, Phys. Rev. Lett. {\bf 110}, 168703 (2013)], a fractal dimension has been proposed to characterize the geometric structure of networks. This measure is an extension to graphs of the so called…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity,…
In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…
In this article, we present a novel box-covering algorithm for analyzing the fractal properties of complex networks. Unlike traditional algorithms that impose a predetermined box size, our approach assigns nodes to boxes identified by their…
This paper presents a versatile model for generating fractal complex networks that closely mirror the properties of real-world systems. By combining features of reverse renormalization and evolving network models, the proposed approach…
Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…