Related papers: Multifractal analysis of complex networks
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar…
The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
We study spatial clustering in a discrete, one-dimensional, stochastic, toy model of heavy particles in turbulence and calculate the spectrum of multifractal dimensions $D_q$ as functions of a dimensionless parameter, $\alpha$, that plays…
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…
This paper is an extensive survey of literature on complex network communities and clustering. Complex networks describe a widespread variety of systems in nature and society especially systems composed by a large number of highly…
The constant increase in the complexity of data networks motivates the search for strategies that make it possible to reduce current monitoring times. This paper shows the way in which multilayer network representation and the application…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range of tools and techniques for time series analysis already exist, the increasing…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
Complex networks pervade various real-world systems, from the natural environment to human societies. The essence of these networks is in their ability to transition and evolve from microscopic disorder-where network topology and node…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the coevolution of topology and weight. In the model, we have the degree distribution exponent $\gamma$ restricted to a range between 2…
Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical…
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…