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.
Internet connectivity at the AS level, defined in terms of pairwise logical peering relationships, is constantly evolving. This evolution is largely a response to economic, political, and technological changes that impact the way ASs conduct their business. We present a new framework for modeling this evolutionary process by identifying a set of criteria that ASs consider either in establishing a new peering relationship or in reassessing an existing relationship. The proposed framework is intended to capture key elements in the decision processes underlying the formation of these relationships. We present two decision processes that are executed by an AS, depending on its role in a given peering decision, as a customer or a peer of another AS. When acting as a peer, a key feature of the AS’s corresponding decision model is its reliance on realistic inter-AS traffic demands. To reflect the enormous heterogeneity among customer or peer ASs, our decision models are flexible enough to accommodate a wide range of AS-specific objectives. We demonstrate the potential of this new framework by considering different decision models in various realistic “what if” experiment scenarios. We implement these decision models to generate and study the evolution of the resulting AS graphs over time, and compare them against observed historical evolutionary features of the Internet at the AS level. Characterizing the evolution of Internet topology is important to our understanding of the Internet architecture and its interplay with technical, economic and social forces. A major challenge in obtaining empirical data on topology evolution is to identify real topology changes from the observed topology changes, since the latter can be due to either topology changes or transient routing dynamics. In this paper, we formulate the topology liveness problem and propose a solution based on the analysis of BGP data. We find that the impact of transient routing dynamics on topology observation decreases exponentially over time, and that the real topology dynamics consist of a constant-rate birth process and a constant-rate death process. Our model enables us to infer real topology changes from observation data with a given confidence level. We demonstrate the usefulness of the model by applying it to three applications: providing more accurate views of the topology, evaluating theoretical evolution models, and empirically characterizing the trends of topology evolution. We find that customer networks and provider networks have distinct evolution trends, which can provide an important input to the design of future Internet routing architecture. We show that the Internet topology at the autonomous system (AS) level has a rich-club phenomenon. The rich nodes, which are a small number of nodes with large numbers of links, are very well connected to each other. The rich-club is a core tier that we measured using the rich-club connectivity and the node-node link distribution. We obtained this core tier without any heuristic assumption between the ASs. The rich-club phenomenon is a simple qualitative way to differentiate between power law topologies and provides a criterion for new network models. To show this, we compared the measured rich-club of the AS graph with networks obtained using the Baraba spl acute si-Albert (BA) scale-free network model, the Fitness BA model and the Inet-3.0 model. 