Related papers: An evolutionary model of long tailed distributions…
Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…
Abel-Tauberian theorems relate power law behavior of distributions and their transforms. We formulate and prove a multivariate version for non-standard regularly varying measures on $\mathbb{R}_+^p$ and then apply it to prove that the joint…
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…
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…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
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 version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
When modeling a directed social network, one choice is to use the traditional preferential attachment model, which generates power-law tail distributions. In a traditional directed preferential attachment, every new edge is added…
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…
We propose a preferential attachment model for network growth where new entering nodes have a partial information about the state of the network. Our main result is that the presence of bounded information modifies the degree distribution…
The Matthew effect describes the phenomenon that in societies the rich tend to get richer and the potent even more powerful. It is closely related to the concept of preferential attachment in network science, where the more connected nodes…
We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…
Recently, increasing empirical evidence indicates the extensive existence of heavy tails in the interevent time distributions of various human behaviors. Based on the queuing theory, the Barab\'asi model and its variations suggest the…
We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount…
Recently several authors have proposed stochastic models of the growth of the Web graph that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer''…
Numerous works have been proposed to generate random graphs preserving the same properties as real-life large scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs…
Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment…