The rich-club phenomenon in the Internet topology

By Shi Zhou, Raul J. Mondragón. IEEE Communications Letters, 2003

551 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ec360154966c740bd0b5f80e9572f577a4ff51fd

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Citations in the corpus

Structure and dynamics of core/periphery networks (2013, background): “If Φ(k) = 0 the nodes do not share any links, if Φ(k) = 1 the rich nodes form a fully connected subnetwork, a clique [3].”
Identifying influential nodes in complex networks (2012, background): “9, we report the ranking-based rich-club phenomenon [39], where ρ(ψ) is the density of connections among the ( 1 − ψ) top-ranked nodes.”
Random walks and diffusion on networks (2016, methodology): “etworks into a Euclidean feature space [415]. It may also be fruitful to exploit similar ideas to examine other types of network properties (e.g., \role similarity" [349, 416], \rich clubs" [417, 418], and approximately multipartite structure [419]). RWs have also been used for some studie”
Critical phenomena in complex networks (2007, background): “In a scale-free network, hubs may form a highly connected cluster (the rich-club phenomenon (Colizza et al., 2006; Zhou and Mondragón, 2004)).”
Characterization of complex networks: A survey of measurements (2005, background): “This phenomenon, known as rich-club, can be measured by the rich-club coefficient, introduced by Zhou and Mondragon [77].”
Vital nodes identification in complex networks (2016, methodology): “However, this method could be inefficient since the nodes of the highest degrees (or other centrality measures) may be highly clustered as indicated by the rich-club phenomenon [183, 184], so that to target all of them is unnecessary.”
Link Prediction in Complex Networks: A Survey (2010, background): “Empirical data has demonstrated that the number of airline flights is not very sensitive to the geographical distancewithin a big range [59,60] (another topological evidence for the relatively good performance of PA on USAir is the so-called rich-club phenomenon [61,62]).”
Rich-Club Organization of the Human Connectome (2011, background): “Failure of a hub can have a severe effect on the level of global communication efficiency of a network, due to its central role in the network (Albert et al., 2000; Callaway et al., 2000; Zhou and Mondragon, 2004).”
Network resilience (2020, background): “At the autonomous system (AS) level of Internet topology, the core tiers between nodes show the rich-club property [602].”
Analyzing and modeling real-world phenomena with complex networks: a survey of applications (2007, background): “The rich-club phenomenon was identified in an AS network, whe re the highest degree nodes are well connected with each other [190].”
Exploring the structure of the U.S. intercity passenger air transportation network: a weighted complex network approach (2008, background): “This ‘‘rich-club phenomenon’’ ( Zhou and Mondragon 2004 ), which occurs when wellconnected vertices tend to form interconnections among each other, was also observed in worldwide airport network (Barrat et al. 2004a) and in India’s airport network (Bagler 2008).”