Alderson, D.Chang, H.Roughan, M.Uhlig, S.Willinger, W.2007-07-102007-07-102006Networks and Heterogeneous Media, 2006; 1(4):569-6001556-18011556-181Xhttp://hdl.handle.net/2440/36186The Internet’s layered architecture and organizational structure give rise to a number of different topologies, with the lower layers defining more physical and the higher layers more virtual/logical types of connectivity structures. These structures are very dif-ferent, and successful Internet topology modeling requires annotating the nodes and edges of the corresponding graphs with information that reflects their network-intrinsic meaning. These structures also give rise to different representations of the traffic that traverses the heterogeneous Internet, and a traffic matrix is a compact and succinct description of the traffic exchanges between the nodes in a given connectivity structure. In this paper, we summarize recent advances in Internet research related to (i) inferring and modeling the router-level topologies of individual service providers (i.e., the physical connectivity structure of an ISP, where nodes are routers/switches and links represent physical connections), (ii) estimating the intra-AS traffic matrix when the AS’s router-level topology and routing configuration are known, (iii) inferring and modeling the Internet’s AS-level topology, and (iv) estimating the inter-AS traffic matrix. We will also discuss recent work on Internet connectivity structures that arise at the higher layers in the TCP/IP protocol stack and are more virtual and dynamic; e.g., overlay networks like the WWW graph, where nodes are web pages and edges represent existing hyperlinks, or P2P networks like Gnutella, where nodes represent peers and two peers are connected if they have an active network connection.en© American Institute of Mathematical SciencesInternet topology, network tomography, traffic matrix, gravity model, model validation.Journal article002006273010.3934/nhm.2006.1.56900024450370000451409Roughan, M. [0000-0002-7882-7329]