There are few studies that look closely at how the topology of the Internet evolves over time; most focus on snapshots taken at a particular point in time. In this paper, we investigate the evolution of the topology of the Autonomous Systems graph of the Internet, examining how eight commonly-used topological measures change from January 2002 to January 2010. We find that the distributions of most of the measures remain unchanged, except for average path length and clustering coefficient. The average path length has slowly and steadily increased since 2005 and the average clustering coefficient has steadily declined. We hypothesize that these changes are due to changes in peering policies as the Internet evolves. We also investigate a surprising feature, namely that the maximum degree has changed little, an aspect that cannot be captured without modeling link deletion. Our results suggest that evaluating models of the Internet graph by comparing steady-state generated topologies to snapshots of the real data is reasonable for many measures. However, accurately matching time-variant properties is more difficult, as we demonstrate by evaluating ten well-known models against the 2010 data.
In this paper, we empirically study the evolution of large scale Internet topology at the autonomous system (AS) level. The network size grows in an exponential form, obeying the famous Moore's law. We theoretically predict that the size of the AS-level Internet will double every 5.32 years. We apply the k-core decomposition method on the real Internet, and find that the size of a k-core with larger k is nearly stable over time. In addition, the maximal coreness is very stable after 2003. In contrast to the predictions of most previous models, the maximal degree of the Internet is also relatively stable versus time. We use the edge-exchange operation to obtain the randomized networks with the same degree sequence. A systematical comparison is drawn, indicating that the real Internet is more loosely connected, and both the full Internet and the nucleus are more disassortative than their randomized versions.