This chapter introduces a recently discovered structure of the Internet, namely the rich-club phenomenon (Zhou & Mondragón, 2004a). The significance of this discovery is that an appreciation of the rich-club phenomenon is essential for a proper examination of global Internet characteristics, such as routing efficiency, network flexibility, and robustness (Zhou & Mondragón, 2004b). Today, rich-club connectivity has been adopted by the networks research community as a topology metric to characterise the Internet structure (Mahadevan et al., 2005).
Key Terms in this Chapter
Statistical Physics: One of the fundamental theories of physics. It uses methods of statistics in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature.
Topology: A connectivity graph representing a real network, upon which the network’s physical and engineering properties are based.
Degree: Is defined, in the graph theory, as the number of connections that a node has, or the number of direct neighbours of the node.
Disassortative Mixing: Describes a statistic behaviour where high-degree nodes tend to connect with low-degree nodes and visa versa. It is found in biological and telecommunications networks, such as the Internet.
Scale-Free Network: A network characterised by a power-law distribution of node degree, where the power-law exponent is invariant to the network size (scale).
Rich-Club Phenomenon: A topology property of some complex networks, which describes the fact that well-connected nodes, “rich” nodes, are tightly interconnected with other rich nodes, forming a core group or club.
BGP: Border gateway protocol, which is the core routing protocol of the Internet. It works by maintaining a table of IP networks or “prefixes” which designate network reachability between autonomous systems (AS).
Small-World Network: A network in which, on average, any two nodes are separated by a very small number of connections.
Short Cycles: Include triangles and quadrangles, which encode the redundancy information in a network, because the multiplicity of paths between any two nodes increases with the density of short cycles.
Autonomous System: A collection of IP networks and routers under the control of one entity (or sometimes more) that presents a common routing policy to the Internet.
CAIDA: Cooperative Association for Internet Data Analysis, which is based at the San Diego Supercomputer Center, U.S. CAIDA is a world-leading organisation for Internet measurement and research.