Comparing static and dynamic measurements and models of the internet's AS topology

Capturing a precise snapshot of the Internet's topology is nearly impossible. Recent efforts have produced autonomous-system (AS) level topologies with noticeably divergent characteristics even calling into question the widespread belief that the Internet's degree distribution follows a power law. In turn, this casts doubt on Internet modeling efforts, since validating a model on one data set does little to ensure validity on another data set, or on the (unknown) actual Internet topology. We examine six metrics - three existing metrics and three of our own - applied to two large publicly-available topology data sets. Certain metrics highlight differences between the two topologies, while one of our static metrics and several dynamic metrics display an invariance between the data sets. Invariant metrics may capture properties inherent to the Internet and independent of measurement methodology, and so may serve as better gauges for validating models. We continue by testing nine models - seven existing models and two of our own - according to these metrics applied to the two data sets. We distinguish between growth models that explicitly add nodes and links over time in a dynamic process, and static models that add all nodes and links in a batch process. All existing growth models show poor performance according to at least one metric, and only one existing static model, called Inet, matches all metrics well. Our two new models - growth models that are modest extensions of one of the simplest existing growth models - perform better than any other growth model across all metrics. Compared with Inet, our models are very simple. As growth models, they provide a possible explanation for the processes underlying the Internet's growth, explaining, for example, why the Internet's degree distribution is more skewed than baseline models would predict.