Related papers: A Note on Power-Laws of Internet Topology
A model for directed networks is proposed and power laws for their in-degree and/or out-degree distributions are derived from the model. It is based on the Barabasi-Albert model and contains two parameters. The parameters serve as…
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…
This paper takes a critical look at the usefulness of power law models of the Internet. The twin focuses of the paper are Internet traffic and topology generation. The aim of the paper is twofold. Firstly it summarises the state of the art…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
The topology of the Internet has typically been measured by sampling traceroutes, which are roughly shortest paths from sources to destinations. The resulting measurements have been used to infer that the Internet's degree distribution is…
Are biological networks different from other large complex networks? Both large biological and non-biological networks exhibit power-law graphs (number of nodes with degree k, N(k) ~ k-b) yet the exponents, b, fall into different ranges.…
The topological (graph) structure of complex networks often provides valuable information about the performance and vulnerability of the network. However, there are multiple ways to represent a given network as a graph. Electric power…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
We evaluate analytically and numerically the size of the frozen core and various scaling laws for critical Boolean networks that have a power-law in- and/or out-degree distribution. To this purpose, we generalize an efficient method that…
The power flow equations, which relate power injections and voltage phasors, are at the heart of many electric power system computations. While Newton-based methods typically find the "high-voltage" solution to the power flow equations,…
During the last three decades the Internet has experienced fascinating evolution, both exponential growth in traffic and rapid expansion in topology. The size of the Internet becomes enormous, yet the network is very `small' in the sense…
More than one billion data sampled with different frequencies from several financial instruments were investigated with the aim of testing whether they involve power law. As a result, a known power law with the power exponent around -4 was…
Power laws are a characteristic distribution that are ubiquitous, in that they are found almost everywhere, in both natural as well as in man-made systems. They tend to emerge in large, connected and self-organizing systems, for example,…
How are people linked in a highly connected society? Since in many networks a power-law (scale-free) node-degree distribution can be observed, power-law might be seen as a universal characteristics of networks. But this study of…
Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper…
We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…
Power law distribution is common in real-world networks including online social networks. Many studies on complex networks focus on the characteristics of vertices, which are always proved to follow the power law. However, few researches…
Power-law networks such as the Internet, terrorist cells, species relationships, and cellular metabolic interactions are susceptible to node failures, yet maintaining network connectivity is essential for network functionality.…
A comparison between the topological properties of the measured Internet topology, at the autonomous system level (AS graph), and the equivalent graphs generated by two different power law topology generators is presented. Only one of the…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…