Related papers: Zipf's law, Hierarchical Structure, and Shuffling-…
Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank. It is very robust as an experimental observation, but to date it escaped…
Previous efforts in complex networks research focused mainly on the topological features of such networks, but now also encompass the dynamics. In this Letter we discuss the relationship between structure and dynamics, with an emphasis on…
Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
We study rank-size distribution of cities in Japan on the basis of data analysis. From the census data after World War II, we find that the rank-size distribution of cities is composed of two parts, each of which has independent power…
The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the systems behavior. In addition, empirical data typically…
Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints. We show that Gibrat's rule, at all…
Human language, as a typical complex system, its organization and evolution is an attractive topic for both physical and cultural researchers. In this paper, we present the first exhaustive analysis of the text organization of human speech.…
It is very important to understand urban mobility patterns because most trips are concentrated in urban areas. In the paper, a new model is proposed to model collective human mobility in urban areas. The model can be applied to predict…
Half of the world population resides in cities and urban segregation is becoming a global issue. One of the best known attempts to understand it is the Schelling model, which considers two types of agents that relocate whenever a transfer…
The presence of hierarchy in many real-world networks is not yet fully explained. Complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for…
We study the time evolution of perturbations in spatially extended chaotic systems in the presence of quenched disorder. We find that initially random perturbations tend to exponentially localize in space around static pinning centers that…
We investigate spatial dependence in Zipf's law for cities among the OECD countries. The aim is to identify an upper tail of the distribution that follows a power law (Pareto) but is perturbed by spatial autocorrelation, as indicated by a…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…
We analyse the statistical properties of public transport networks. These networks are defined by a set of public transport routes (bus lines) and the stations serviced by these. For larger networks these appear to possess a scale-free…
This article analyzes the complex geometry of urban transportation networks as a gateway to understanding their encompassing urban systems. Using a proposed ring-buffer approach and applying it to 50 urban areas in the United States, we…
History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their sample-space, or…
We show that the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity are related to the focal expression of a generalized thermodynamic structure. This…
We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock…