Related papers: A Generalized Preferential Attachment Model for Bu…
We propose a growing network model for a community with a group structure. The community consists of individual members and groups, gatherings of members. The community grows as a new member is introduced by an existing member at each time…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…
In the last years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipf's systems, due to the discreteness of the variables and to the existence of two representations…
We study a generalization of the Wolf-Villain (WV) interface growth model based on a probabilistic growth rule. In the WV model, particles are randomly deposited onto a substrate and subsequently move to a position nearby where the binding…
We study a discrete-time stochastic process that can also be interpreted as a model for a viral evolution. A distinguishing feature of our process is power-law tails due to dynamics that resembles preferential attachment models. In the…
A variation of the preferential attachment random graph model of Barab\'asi and Albert is defined that incorporates planted communities. The graph is built progressively, with new vertices attaching to the existing ones one-by-one. At every…
A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called…
Zipf's law states that the probability of a variable being larger than $s$ is roughly inversely proportional to $s$. In this paper, we evaluate Zipf's law for the distribution of firm size by the number of employees in Brazil. We use…
The distribution of the population of cities has attracted a great deal of attention, in part because it sharply constrains models of local growth. However, to this day, there is no consensus on the distribution below the very upper tail,…
We study a new class of preferential attachment trees with \emph{self-reinforcement}. At each time, each vertex is assigned a weight equal to the cumulative sum over past times of an affine function of its degree. A new vertex attaches…
The rank-size distribution of cities follows Zipf's law, and the Zipf scaling exponent often tends to a constant 1. This seems to be a general rule. However, a recent numerical experiment shows that there exists a contradiction between the…
Growing synthetic networks that follow power law distributions of a node's degree often involves adding one node at a time. Each node is added to the network with a fixed amount of edges and those edges are frozen for all future time steps.…
We propose hypotheses describing the empirical finding of an association between the exponents of urban GDP scaling and Zipf's law for cities. These hypotheses represent various combinations of directional or reciprocal causal links between…
We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness…
We propose a new preferential attachment-based network growth model in order to explain two properties of growing networks: (1) the power-law growth of node degrees and (2) the decay of node relevance. In preferential attachment models, the…
In order to better understand dynamical functions on amounts of natural and man-made complex systems, lots of researchers from a wide range of disciplines, covering statistic physics, mathematics, theoretical computer science, and so on,…
Suppose in a graph $G$ vertices can be either red or blue. Let $k$ be odd. At each time step, each vertex $v$ in $G$ polls $k$ random neighbours and takes the majority colour. If it doesn't have $k$ neighbours, it simply polls all of them,…
This paper analyzes key properties of networks generated by geometric preferential attachment. We establish that the expected number of triangles is proportional to that of the standard preferential attachment model, with a proportionality…
A microscopic model of aggregation and fragmentation is introduced to investigate the size distribution of businesses. In the model, businesses are constrained to comply with the market price, as expected by the customers, while customers…
This paper introduces an approach to reference class selection in distributional forecasting with an application to corporate sales growth rates using several co-variates as reference variables, that are implicit predictors. The method can…