Related papers: A Stochastic Model for the Evolution of the Web
We present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
We study an agent-based model of evolution of wealth distribution in a macro-economic system. The evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth and interactions between agents. We…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…
Reproductive success and survival are influenced by wealth in human populations. Wealth is transmitted to offsprings and strategies of transmission vary over time and among populations, the main variation being how equally wealth is…
Classical rich-get-richer models have found much success in being able to broadly reproduce the statistics and dynamics of diverse real complex systems. These rich-get-richer models are based on classical urn models and unfold step-by-step…
Disentangling the mechanisms underlying the social network evolution is one of social science's unsolved puzzles. Preferential attachment is a powerful mechanism explaining social network dynamics, yet not able to explain all scaling-laws…
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…
A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…
This paper is concerned with general spatially explicit versions of three stochastic models for the dynamics of money that have been introduced and studied numerically by statistical physicists: the uniform reshuffling model, the immediate…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat's law of proportionate effects as the result of…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
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…
We propose a bare-bones stochastic model that takes into account both the geographical distribution of people within a country and their complex network of connections. The model, which is designed to give rise to a scale-free network of…
We propose a model for the World Wide Web graph that couples the topological growth with the traffic's dynamical evolution. The model is based on a simple traffic-driven dynamics and generates weighted directed graphs exhibiting the…
The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…