A Stochastic Evolutionary Model Exhibiting Power-Law Behaviour with an Exponential Cutoff

We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on popularity-driven and fitness-driven preferential attachments. As the network grows, a newly added node establishes $m$ new links to existing nodes with a probability $p$ based on popularity of the existing nodes and a probability $1-p$ base...

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 allows new underlying generative network models to be explored. The preferential attachment model is a natural starting point for these models. This work adds additional model components to account for observed phenomena in the distributions....

In several real-world networks like the Internet, WWW etc., the number of links grow in time in a non-linear fashion. We consider growing networks in which the number of outgoing links is a non-linear function of time but new links between older nodes are forbidden. The attachments are made using a preferential attachment scheme. In the deterministic picture, the number of outgoing links $m(t)$ at any time $t$ is taken as $N(t)^\theta$ where $N(t)$ is the number of nodes pres...

A new mechanism leading to scale-free networks is proposed in this letter. It is shown that in many cases of interest, the connectivity power-law behavior is neither related to dynamical properties nor to preferential attachment. Instead, we show that without increasing the number of vertices in time and without applying the so called {\it ``rich-get-richer''} condition we obtain networks whose statistical properties are scale-free. Assigning a quenched fitness value $x_i$ to...

In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or...

We investigate choice-driven network growth. In this model, nodes are added one by one according to the following procedure: for each addition event a set of target nodes is selected, each according to linear preferential attachment, and a new node attaches to the target with the highest degree. Depending on precise details of the attachment rule, the resulting networks has three possible outcomes: (i) a non-universal power-law degree distribution; (ii) a single macroscopic h...

We propose a simple dynamical model that generates networks with power-law degree distributions with the exponent 2 through rewiring only. At each time step, two nodes, i and j, are randomly selected, and one incoming link to i is redirected to j with the rewiring probability R, determined only by degrees of two nodes, k_i and k_j, while giving preference to high-degree nodes. To take the structure of networks into account, we also consider what types of networks are of inter...

Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their validity. We show that main properties of scale-free evolving networks may be described in frames of a simple continuous approach. The simplest models of networks, which growth is determined by a mechanism of preferential linking, are used. We cons...

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number ...

Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law property. First, we study a class of birth-and-death networks that is ubiquitous in the real world, and calculate its degree distributions. Our results show that the tails of its degree distributions exhibits a distinct power law feature, providi...