Related papers: Power Laws, the Price Model, and the Pareto type-2…
We introduce a new analytical framework for modelling degree sequences in individual communities of real-world networks, e.g., citations to papers in different fields. Our work is inspired by a recent modification of the Price's model,…
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two…
Using a model of wealth distribution where traders are characterized by quenched random saving propensities and trade among themselves by bipartite transactions, we mimic the enhanced rates of trading of the rich by introducing the…
The rich-get-richer mechanism (agents increase their ``wealth'' randomly at a rate proportional to their holdings) is often invoked to explain the Pareto power-law distribution observed in many physical situations, such as the degree…
This paper analyzes a variation on the well-known "power of two choices" allocation algorithms. Classically, the smallest of $d$ randomly-chosen options is selected. We investigate what happens when the largest of $d$ randomly-chosen…
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 show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random saving propensities in an ideal gas-like market model and (ii)…
Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
We propose a simple preferential attachment model of growing network using the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i) \propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are preferentially…
A model based on first-degree family relations network is used to describe the wealth distribution in societies. The network structure is not a-priori introduced in the model, it is generated in parallel with the wealth values through…
We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…
Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is ``interrupted'' by a sharp cut-off in its upper tail, where it is totally…
We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a…
A mechanism is proposed for the appearance of power law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law…
In the double rank analysis of research publications, the local rank position of a country or institution publication is expressed as a function of the world rank position. Excluding some highly or lowly cited publications, the double rank…
Rankings on online platforms help their end-users find the relevant information -- people, news, media, and products -- quickly. Fair ranking tasks, which ask to rank a set of items to maximize utility subject to satisfying group-fairness…
A computational model for the distribution of wealth among the members of an ideal society is presented. It is determined that a realistic distribution of wealth depends upon two mechanisms: an asymmetric flux of wealth in trading…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…