Efficient network generation under general preferential attachment

Abstract

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 by sequentially introducing nodes that attach preferentially to existing nodes with high degree. 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, provides efficient data structures that work under any preference function, and presents 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 (10 6 to 10 8 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.

Fitting the linear preferential attachment model

“…A similar idea for the simulation of the Yule-Simon process appeared in [20]. Efficient simulation methods for the case where the preferential attachment probabilities are non-linear are studied in [1], where their algorithm trades some efficiency for the flexibility to model non-linear preferential attachment. Using the notation from the introduction, at time t = 0, we initiate with an arbitrary graph G(n 0 ) = (V (n 0 ), E(n 0 )) of n 0 edges, where the elements of E(n 0 ) are represented in form of (v…”

“…Hence it is important to have efficient simulation algorithms for producing realizations of the preferential attachment network for a given set of parameter values. We adopt a simulation method, learned from Joyjit Roy, that was inspired by [1] and is similar to that of [20].…”

A high-level and scalable approach for generating scale-free graphs using active objects

“…There exist some attempts to develop efficient implementations of the PA model [2,5,8,16,21,22,25,27]. Some existing works focus on more efficient implementations of the sequential version [5,8,25]. Such methods propose the utilization of data-structures that are efficient with respect to memory consumption and time complexity.…”

Network characteristics emerging from agent interactions in balanced distributed system

“…The Barabàsi–Albert model is characterized by the features of scale-free and preferential attachment. Many real networks like the web [ 13 ], the Internet [ 17 ], and some social networks [ 18 ] exhibit these features. Random graphs are a general model that can be used as a reference for most real network types.…”