Why the Internet is so small?

arXiv:1003.5803v1 [cs.NI] 30 Mar 2010 Why the Internet is so ‘small’? Shi Zhou Department of Computer Science, University College London Malet Place, London, WC1E 6BT, United Kingdom s.zhou@cs.ucl.ac.uk Abstract. During the last three decades the Internet has experienced fascinating evolution, both exponential growth in traffic and rapid ex- pansion in topology. The size of the Internet becomes enormous, yet the network is very ‘small’ in the sense that it is extremely efficient to route data packets across the global Internet. This paper provides a brief re- view on three fundamental properties of the Internet topology at the autonomous systems (AS) level. Firstly the Internet has a power-law de- gree distribution, which means the majority of nodes on the Internet AS graph have small numbers of links, whereas a few nodes have very large numbers of links. Secondly the Internet exhibits a property called disas- sortative mixing, which means poorly-connected nodes tend to link with well-connected nodes, and vice versa. Thirdly the best-connected nodes, or the rich nodes, are tightly interconnected with each other forming a rich-club. We explain that it is these structural properties that make the global Internet so ‘small’. Key words: Internet, network, topology, autonomous systems, BGP, shortest path, power-law, scale-free, assortative mixing, rich-club 1 Introduction The Internet is a network of autonomous systems (AS) which are collections of IP networks and routers under the control of one entity, typically an Internet service provider. The Border Gateway Protocol (BGP) is a critical component of the Internet’s infrastructure as it serves to connect these ASes together [1]. Performance of the BGP depends strongly on properties of the topological con- nectivity between these ASes. Surprisingly, it was only in 1999 that researchers reported that the Internet AS graph is a ‘scale-free’ network [2]. This discovery effectively invalidated all previous Internet models based on random graphs. Since then researchers have reported many other topological properties of the Internet [3, 4]. In this paper we review three of them, namely the power- law degree distribution [5], the disassortative mixing [6, 7] and the rich-club phenomenon [8]. We explain that it is these structural properties that make the global Internet so ‘small’ in the sense that it is extremely efficient to route data packets across the global Internet. So far much of the research on Internet topology occurs in the communities of physics, mathematics and complexity science. Interdisciplinary communica- 2 Shi Zhou tion with other communities is much needed [9]. This paper is an effort towards this direction. The network under study is the Internet, but the statistical meth- ods and the topological properties introduced here can be applied to any other network in nature and society. 2 Internet Topology at AS Level BGP peering Fig. 1. Nodes of the Internet topology. (1) Hosts, that are the computers of users; (2) routers, that arrange data traffic across the Internet; and (3) autonomous systems (AS) that are subnetworks in the Internet. The Internet is a capital example of complex networks. It is unlike any pre- vious human invention in both scale and effect, and is now a global resource important to all of the people in the world. The Internet provides a low-level communication infrastructure upon which other communication mechanisms can be built, e.g. the ubiquitous email and Web protocols. Internet service providers (ISP) offer billions of users access to the Internet via telephone line, cable and wireless connections. Data packets generated by users are forwarded across the Internet toward their destinations by routers through a process known as rout- ing. The Internet contains millions of routers, which are grouped into thousands of subnetworks, called autonomous systems (AS) (see Fig. 1). The global Internet structure is characterised at the AS-level because the delivery of data traffic through the Internet depends on the complex interactions between ASes that exchange routing information using the Border Gateway Protocol (BGP). On the Internet AS-level topology, a node is an AS, which is usually controlled by an ISP; and a link represents a BGP peering relation between two ASes, which a commercial agreement between two ISPs on forwarding data traffic. Measurement data of the Internet AS-level topology became available in late 1990’s. Since then there have been a number of projects to collect the topol- Internet Topology 3 ogy data of the Internet [4]. These measurements have greatly improved our understanding of the structure and evolution of the Internet [3]. The Internet macroscopic structure has become relatively stable in recent years. This suggests that the Internet has entered a fairly mature stage in terms of network evolution. Today the Internet AS graph is very large. It contains about twenty thousand AS nodes and fifty thousands of links. It is impo

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