Preferential attachment (PA) models of network structure are widely used due to their explanatory power and conceptual simplicity. PA models are able to account for the scale-free degree distributions observed in many real-world large networks through the remarkably simple mechanism of sequentially introducing nodes that attach preferentially to high-degree nodes. The ability to efficiently generate instances from PA models is a key asset in understanding both the models themselves and the real networks that they represent. Surprisingly, little attention has been paid to the problem of efficient instance generation. In this paper, we show that the complexity of generating network instances from a PA model depends on the preference function of the model, provide efficient data structures that work under any preference function, and present empirical results from an implementation based on these data structures. We demonstrate that, by indexing growing networks with a simple augmented heap, we can implement a network generator which scales many orders of magnitude beyond existing capabilities ( @math -- @math nodes). We show the utility of an efficient and general PA network generator by investigating the consequences of varying the preference functions of an existing model. We also provide "quicknet", a freely-available open-source implementation of the methods described in this work.
In this paper, we present a new simulation tool for scale-free networks composed of a high number of nodes. The tool, based on discrete-event simulation, enables the definition of scale-free networks composed of heterogeneous nodes and complex application-level protocols. To satisfy the performance and scalability requirements, the simulator supports both sequential (i.e. monolithic) and parallel distributed (i.e. PADS) approaches. Furthermore, appropriate mechanisms for the communication overhead-reduction are implemented. To demonstrate the efficiency of the tool, we experiment with gossip protocols on top of scale-free networks generated by our simulator. Results of the simulations demonstrate the feasibility of our approach. The proposed tool is able to generate and manage large scale-free networks composed of thousands of nodes interacting following real-world dissemination protocols. Evolution and structure of very large networks has attracted considerable attention in recent years. In this paper we study a possibility to simulate stochastic processes which move edges in a network leading to a scale-free structure. Scale-free networks are characterized by a ''fat-tail'' degree distribution with considerably higher presence of so called hubs - nodes with very high degree. To understand and predict very large networks it is important to study the possibility of parallel simulation. We consider a class of stochastic processes which keeps the number of edges in the network constant called equilibrium networks. This class is characterized by a preferential selection where the edge destinations are chosen according to a preferential function f(k) which depends on the node degree k. For this class of stochastic processes we prove that it is difficult if not impossible to design an exact parallel algorithm if the function f(k) is monotonous with an injective derivative. However, in the important case where f(k) is linear we present a fully scalable algorithm with almost linear speedup. The experimental results confirm the linear scalability on a large processor cluster. We describe how different optimized algorithms may be effective in implementing the preferential attachment mechanism in different cases. We analyze performances with respect to different values of some parameters related to the Yule process associated to the preferential attachment. We examine how performance scales with system size and provide extensive simulations to support our theoretical findings. With the continuous expansion of the network size, some networks gradually present the characteristics of social networks, especially, scale-free networks. At present, some theoretical studies of scale-free networks are mainly based on simulated platforms. Based on this, the question that how we fast simulate a network model possessing scale-free effects and presenting related characteristics of realistic networks in unbiased manner becomes a crucial problem. In the paper, we propose an algorithm, named RX, which can fast locate nodes to simulate a network. Then, we will analysis the characteristics of the network by experiments and compare RX's modeling time with BA's. (BA has become a popular algorithm in simulating scale-free networks.) The characteristics and the comparison can effectively prove that the algorithm we design can fast simulate scale-free networks to provide a good reference in building network models.