A 27-year Longitudinal Study on the Structure of the Internet Topology: Scale-freeness and Preferential Attachment.

Abstract

In this paper, we present a 27-year longitudinal study of the Internet topology at Autonomous System (AS) level, from 1998 to 2025. The Internet has been claimed to be scale-free exhibiting power-law degree distribution. This claim has been challenged from several fronts (e.g., rigor of the statistical method, assumptions made on finiteness of the network, completeness of available data). Using the latest statistical methodology, we revisit and verify whether this claim still holds. Using power-law as the reference distribution, we use maximum-likelihood fitting method with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios to identify the best fitting distribution among several common statistical distributions. In fact, being scale-free directly implies the property would remain over the passage of time and hence, we investigate how this has evolved over the past nearly three decades. We found that power-law is not the best fit for the degree distribution of the Internet. For most years, truncated power-law offers better fit while log-normal is often better than powerlaw. Furthermore, the simple preferential attachment model has been attributed as the underlying generative mechanism that consequently results in the topology we have today. Based on the two methods we used, we found that while there is indication of preferential attachment as previously discovered, this is only true for smaller values of degree rather than the entire distribution and that the attachment behavior hovers between both sub-linear and super-linear attachment regimes at different time points. Finally, we also found that new links do not only tend to attach to high-degree nodes. There is also a large number of new linksbthat join low-degree nodes, contradicting the claim on new nodes prefer to join high-degree nodes. Nevertheless, when weighted by the number of nodes with specific degree ranges, the net effect of “rich-gets-richer” still stands due to imbalance node population across different degrees.