Redundancy and Robustness of the AS-level Internet topology and its models

A comparison between the topological properties of the measured Internet topology, at the autonomous system level (AS graph), and the equivalent graphs generated by two different power law topology generators is presented. Only one of the synthetic generators reproduces the tier connectivity of the AS graph. Introduction: Simulation plays an important role in the development of the Internet, as it can be used to compare and analyze new network protocols. In these simulations it is crucial that the topology generators capture the key topological properties of the Internet. For example, Labovitz et al [1] showed that the topology of the Internet has a major impact on the delayed BGP routing convergence. If each autonomous system (AS) of the Internet is represented by a node in a graph, Faloutsos et al [2] discovered that the link connectivity between these nodes follows the power law P (k) ∝ k , γ ≈ 2.2, where k is the number of links a node has. A good model of the AS-level Internet topology not only has to reproduce the power law link connectivity but also the connectivity of the core of the network. Tier 1 of the AS graph is the core of the network which consists of a set of nodes which are very rich in links and are densely interconnected with each other, we called this set of nodes the rich–club [3]. This letter shows that a power law topology generator without a rich–club could under–estimate network redundancy and over–estimate network robustness of the Internet. TABLE I NETWORK PROPERTIES AS graph IG graph FBA graph Number of nodes, N 11122 11122 11122 Number of links, L 30054 33349 33349 Power–law exponent, γ 2.2 2.22 2.255 Maximum k 2839 842 1793 Maximum Kt 7482 4962 1191 Average Kt 12.7 10.0 0.6 Manuscript received on 19 August 2003, published on 22 January 2004 in IEE Electronic Letters vol. 40, no. 2, pp. 151-15. This work is supported by the U.K. Engineering and Physical Sciences Research Council (EPSRC) under Grant GR-R30136-01. S. Zhou and R. J. Mondragón are with the Department of Electronic Engineering, Queen Mary, University of London, Mile End Road, London, E1 4NS, United Kingdom (e-mail: [email protected]; [email protected]). Methodology: We compared the traceroute AS graph [4] measured on the 1st of April 2002 against the synthetic networks generated by the Fitness Barabási–Albert (FBA) model [5] and Interactive Growth (IG) model [6]. The two models create networks using a node growth mechanism, where a new node attaches to other nodes and prefers to attach itself to nodes that have large numbers of links. The FBA model is an example of a generator where the preferential attachment is controlled by a fitness parameter. This parameter adjust the node’s ability of acquiring connections with other nodes. The IG model is an example of a generator where a new node attaches itself to other nodes and also creates new links between nodes that already exist on the network. As shown in table 1, these two topology models generate networks that have similar sizes and power law degree distributions as the AS graph.