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 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 (10 6 -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…”

“…Research of the four authors was partially supported by Army MURI grant W911NF-12-1-0385. Don Towsley from University of Massachusetts introduced us to the model and within his group, James Atwood graciously supplied us with a simulation algorithm designed for a class of growth models broader than the one specified in Section 2.1; this later became [1]. Joyjit Roy, formerly of Cornell, created an efficient algorithm designed to capitalize on the linear growth structure.…”

“…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].…”

Scalable generation of random graphs

“…Sequential RAM implementations of the BB BA algorithm (or variants of it) appear in a number of network analysis frameworks such as NetworkX [163] or NetworKit [316]. In this context, Atwood et al present a generator for generalized non-linear preferential attachment based on augmented heaps and treaps [25]. For advanced models of computation there are various generation algorithms that do not strictly follow the Barabási-Albert generation rules and hence only yield some approximation.…”