Using a simple deterministic model for the Internet graph we show that the eigenvalue power-law distribution for its adjacency matrix is a direct consequence of the degree distribution and that the graph must contain many star subgraphs.

Power laws in socioeconomic systems are generally explained as being generated by multiplicative growth of aggregate objects. In this paper we formulate a model of geographic activity distribution with spatial correlations on the level of land lots where multiplicative growth is assumed to be...

We propose a simple random process generating various types of random graphs and the scale-free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature before.

Previous work showed how moving particles that rest along their trajectory lead to time-nonlocal advection–dispersion equations. If the waiting times have infinite mean, the model equation contains a fractional time derivative of order between 0 and 1. In this article, we develop a new...

In this paper we introduce a simple model for a financial market characterized by a single stock or good and an interplay between two different trader populations, chartists and fundamentalists, which determine the price dynamics of the stock. The model has been inspired by the microscopic...

In this paper we propose a model based on the Boltzmann distribution as a mechanism for generating power laws, Boltzmann Power Laws (BPL). Some of these power laws are studied and compared to popular power laws such as ‘1/f’ noise and self-organized criticality (SOC). We will show how, in...

The growth and dynamics of solid surfaces displays a multitude of power law relationships, which are often associated with geometric self-similarity. In many cases the mechanisms behind these power laws are comparatively trivial, and require little more than dimensional analysis for their...

A solitary signal created in the horizontal granular chain disperses and damps when it propagates down in the vertical chain because the elastic property of the medium in the vertical chain changes due to gravity. We show that this change in the vertical chain follows power-laws in time,...

This research examines the physical constraints on the growth process. In order to run, maintain and build capital energy is required to be distributed to geographically dispersed sites where investments are deemed profitable. We capture this aspect of physical reality by a network theory of...

Pareto distributions, and power laws in general, have demonstrated to be very useful models to describe very different phenomena, from physics to finance. In recent years, the econophysical literature has proposed a large amount of papers and models justifying the presence of power laws in...