Efficient Network Generation Under General Preferential Attachment

TL;DR

This paper introduces a highly efficient and general method for generating preferential attachment networks, capable of scaling to millions or hundreds of millions of nodes, and provides an open-source implementation.

Contribution

It presents a new data structure based on an augmented heap for efficient PA network generation under any preference function, significantly improving scalability.

Findings

Scales network generation to 10^6 - 10^8 nodes

Supports arbitrary preference functions efficiently

Provides open-source implementation 'quicknet'

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.