The Rich-Club Phenomenon In The Internet Topology

Abstract

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 ASes. 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 Barabási--Albert (BA) scale--free network model, the Fitness BA model and the Inet--3.0 model.

To be appeared in the IEEE Communications Letters

References in corpus (8)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Error and attack tolerance of complex networks
• Assortative mixing in networks
• Mixing patterns in networks
• Mean-field theory for scale-free random networks
• Attack vulnerability of complex networks
• Betweenness centrality correlation in social networks

Cited by in corpus (126)

• Link Prediction in Complex Networks: A Survey
• Characterization of complex networks: A survey of measurements
• Critical phenomena in complex networks
• Predicting Missing Links via Local Information
• Vital nodes identification in complex networks
• Detecting rich-club ordering in complex networks
• Controllability of Brain Networks
• Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications
• Random walks and diffusion on networks
• Emergence of network features from multiplexity
• Inferring Social Status and Rich Club Effects in Enterprise Communication Networks
• Prominence and control: The weighted rich-club effect
• Structure and dynamics of core-periphery networks
• The multilayer connectome of Caenorhabditis elegans
• Empirical analysis of the worldwide maritime transportation network
• Core-periphery organization of complex networks
• Weighted network modules
• Network resilience
• Accurately modeling the Internet topology
• Identification of core-periphery structure in networks
• The International Trade Network: weighted network analysis and modelling
• The rich-club phenomenon across complex network hierarchies
• Computational Socioeconomics
• Modular gateway-ness connectivity and structural core organization in maritime network science
• Social goods dilemmas in heterogeneous societies
• From modular to centralized organization of synchronization in functional areas of the cat cerebral cortex
• Socioeconomic correlations and stratification in social-communication networks
• On the rich-club effect in dense and weighted networks
• A Unifying Framework for Measuring Weighted Rich Clubs
• The Weakness of Weak Ties in the Classroom
• An Experimental Investigation of Hyperbolic Routing with a Smart Forwarding Plane in NDN
• Rich-club connectivity dominates assortativity and transitivity of complex networks
• Structural constraints in complex networks
• Core-periphery structure requires something else in the network
• Complex stock trading network among investors
• Conjoining uncooperative societies facilitates evolution of cooperation
• Multiplex core-periphery organization of the human connectome
• Resilience or Robustness: Identifying Topological Vulnerabilities in Rail Networks
• A new dominance concept and its application to diversity-stability analysis
• Inferring network properties from time series using transfer entropy and mutual information: validation of multivariate versus bivariate approaches
• Rich-club vs rich-multipolarization phenomena in weighted networks
• Synchronization in symmetric bipolar population networks
• Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights
• A critical look at power law modelling of the Internet
• Influence of initial distributions on robust cooperation in evolutionary Prisoner's Dilemma
• VIP-club phenomenon: emergence of elites and masterminds in social networks
• Understanding the internet topology evolution dynamics
• State power and elite autonomy in a networked civil society: The board interlocking of Chinese non-profits
• Topological Structure of Urban Street Networks from the Perspective of Degree Correlations
• Chinese Internet AS-level Topology
• How to become a superhero
• The Temporal Rich Club Phenomenon
• Statistical significance of rich-club phenomena in complex networks
• Phase Changes in the Evolution of the IPv4 and IPv6 AS-Level Internet Topologies
• Information Diffusion in Computer Science Citation Networks
• Empirical study on clique-degree distribution of networks
• Spontaneous Self-Assembly of Transcription Factor Based Gene Regulation Networks
• Rich-Club Ordering and the Dyadic Effect: Two Interrelated Phenomena
• Generalized Rich-Club Ordering in Networks
• The World-Trade Web: Topological Properties, Dynamics, and Evolution
• The wisdom of networks: A general adaptation and learning mechanism of complex systems: The network core triggers fast responses to known stimuli; innovations require the slow network periphery and are encoded by core-remodeling
• Complex network analysis of brain functional connectivity under a multi-step cognitive task
• Geometric explanation of the rich-club phenomenon in complex networks
• Rich-club and page-club coefficients for directed graphs
• Interplay between $k$-core and community structure in complex networks
• Networks with arbitrary edge multiplicities
• Internet Topology over Time
• The AI Community Building the Future? A Quantitative Analysis of Development Activity on Hugging Face Hub
• Extracting the signed backbone of intrinsically dense weighted networks
• Structural Bounds on the Dyadic Effect
• Observability transitions in correlated networks
• Information Filtering on Coupled Social Networks
• Weighted hypersoft configuration model
• Predicting the evolution of complex networks via local information
• The Drivers of Global News Spreading Patterns
• Multilayer network analysis to study complex inter-subsystem interactions in a turbulent thermoacoustic system
• Optimal transport on supply-demand networks
• The missing links in the BGP-based AS connectivity maps
• Higher-order rich-club phenomenon in collaborative research grants
• Optimizing and controlling functions of complex networks by manipulating rich-club connections
• Random Networks with given Rich-club Coefficient
• Filtering higher-order datasets
• Impact of noise and damage on collective dynamics of scale-free neuronal networks
• Complicating the Social Networks for Better Storytelling: An Empirical Study of Chinese Historical Text and Novel
• Modeling the IPv6 Internet AS-level Topology
• Structure constrained by metadata in networks of chess players
• From Caesar to Twitter: An Axiomatic Approach to Elites of Social Networks
• The interconnectedness of the economic content in the speeches of the US Presidents
• Sufficient conditions of endemic threshold on metapopulation networks
• Ranking the Importance of Nodes of Complex Networks by the Equivalence Classes Approach
• Characterizing cycle structure in complex networks
• Characterising Web Site Link Structure
• Detecting network communities via greedy expanding based on local superiority index
• Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
• Fingerprint for Network Topologies
• Why the Internet is so 'small'?
• War pact model of shrinking networks
• Rich-clubness test: how to determine whether a complex network has or doesn't have a rich-club?
• Internet data packet transport: from global topology to local queueing dynamics
• The Atlas for the Aspiring Network Scientist
• Determinable and interpretable network representation for link prediction
• The behavior of rich-club coefficient in scale-free networks
• Ensembles related to the rich-club coefficient for non-evolving networks
• Finding Alternate Paths in the Internet:A Survey of Techniques for End-to-End Path Discovery
• Information content based model for the topological properties of the gene regulatory network of Escherichia coli
• Temporal rich club phenomenon and its formation mechanisms
• On the location and the strength of controllers to desynchronize coupled Kuramoto oscillators
• Degree and connectivity of the Internet's scale-free topology
• Network Null Model based on Maximal Entropy and the Rich-Club
• The spark of synchronization in heterogeneous networks of chaotic maps
• Computational Human Dynamics
• Learning an Integrated Distance Metric for Comparing Structure of Complex Networks
• Ensembles based on the Rich-Club and how to use them to build soft-communities
• High Performance Algorithms for Quantum Gravity and Cosmology
• Inferring Internet AS Relationships Based on BGP Routing Policies
• Modelling Multi-Trait Scale-free Networks by Optimization
• A scientific understanding of network designing
• Disjoint-Path Selection in Internet: What traceroutes tell us?
• Dense and sparse vertex connectivity in networks
• Funding shapes the anatomy of scientific research
• Being Central on the Cheap: Stability in Heterogeneous Multiagent Centrality Games
• Extrema Analysis of Node Centrality in Weighted Networks
• Observation of complex functional cortical patterns in brain cognition
• Towards a Quantitative Theory of Digraph-Based Complexes and its Applications in Brain Network Analysis
• On Rich Clubs of Path-Based Centralities in Networks
• Scale-Invariant Strength Assortativity of Streaming Butterflies