Large-scale topological and dynamical properties of Internet

Abstract

We study the large-scale topological and dynamical properties of real Internet maps at the autonomous system level, collected in a three years time interval. We find that the connectivity structure of the Internet presents average quantities and statistical distributions settled in a well-defined stationary state. The large-scale properties are characterized by a scale-free topology consistent with previous observations. Correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the Internet. The study of the Internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models. We compare the properties of growing network models with the present real Internet data analysis.

13 pages, 15 eps figures

References in corpus (11)

• Statistical mechanics of complex networks
• Evolution of networks
• Who is the best connected scientist? A study of scientific coauthorship networks
• Dynamical and correlation properties of the Internet
• Universal Behavior of Load Distribution in Scale-free Networks
• Search in Power-Law Networks
• Modeling the Internet's Large-Scale Topology
• Measuring preferential attachment for evolving networks
• Fluctuation-driven dynamics of the Internet topology
• Intentional Walks on Scale Free Small Worlds
• A Note on Power-Laws of Internet Topology

Cited by in corpus (214)

• The structure and function of complex networks
• The architecture of complex weighted networks
• Hierarchical organization of modularity in metabolic networks
• Epidemic processes in complex networks
• Link Prediction in Complex Networks: A Survey
• Spatial Networks
• Hierarchical Organization in Complex Networks
• The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles
• Detecting rich-club ordering in complex networks
• Recommender Systems
• Statistical physics of vaccination
• Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications
• Generation of uncorrelated random scale-free networks
• Betweenness Centrality in Large Complex Networks
• Topology of the World Trade Web
• Modeling bursts and heavy tails in human dynamics
• Growing networks with local rules: preferential attachment, clustering hierarchy and degree correlations
• Epidemic spreading in correlated complex networks
• Absence of epidemic threshold in scale-free networks with connectivity correlations
• Analysis of the Airport Network of India as a complex weighted network
• Class of correlated random networks with hidden variables
• Statistical analysis of 22 public transport networks in Poland
• Classes of complex networks defined by role-to-role connectivity profiles
• A Tutorial in Connectome Analysis: Topological and Spatial Features of Brain Networks
• Pattern Detection in Complex Networks: Correlation Profile of the Internet
• Detecting communities in large networks
• Preferential attachment in the growth of social networks: the case of Wikipedia
• Modeling the evolution of weighted networks
• Spectra of complex networks
• Synchronization of Kuramoto Oscillators in Scale-Free Networks
• Graph Metrics for Temporal Networks
• Fluctuations in network dynamics
• Self-organization of collaboration networks
• Epidemic spreading in complex networks with degree correlations
• Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations
• Accurately modeling the Internet topology
• Congestion and centrality in traffic flow on complex networks
• Critical load and congestion instabilities in scale-free networks
• Epidemic spreading on complex networks with community structures
• Network analysis identifies weak and strong links in a metapopulation system
• On the Origins of Hierarchy in Complex Networks
• All scale-free networks are sparse
• Clustering in complex networks. I. General formalism
• Structure of a large social network
• Percolation on correlated networks
• Tuning clustering in random networks with arbitrary degree distributions
• Separating internal and external dynamics of complex systems
• Topology and Evolution of Technology Innovation Networks
• Systematic Topology Analysis and Generation Using Degree Correlations
• Compact Routing on Internet-Like Graphs
• The effects of spatial constraints on the evolution of weighted complex networks
• Weighted Assortative And Disassortative Networks Model
• Exploring networks with traceroute-like probes: theory and simulations
• Transport on Complex Networks: Flow, Jamming and Optimization
• How clustering affects the bond percolation threshold in complex networks
• The evolutionary origins of hierarchy
• The effect of aging on network structure
• Correlations in weighted networks
• Structural transitions in scale-free networks
• Folks in Folksonomies: Social Link Prediction from Shared Metadata
• Rate equation approach for correlations in growing network models
• Bond percolation on a class of clustered random networks
• Diffusion-annihilation processes in complex networks
• Polynomial growth in age-dependent branching processes with diverging reproductive number
• Heterogeneous Bond Percolation on Multitype Networks with an Application to Epidemic Dynamics
• Clustering of correlated networks
• Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect
• Emergence of Soft Communities from Geometric Preferential Attachment
• Topology and correlations in structured scale-free networks
• Characterizing the network topology of the energy landscapes of atomic clusters
• Mesoscopic organization reveals the constraints governing C. elegans nervous system
• Triadic closure dynamics drives scaling-laws in social multiplex networks
• Complex earthquake networks: Hierarchical organization and assortative mixing
• Structure of Peer-to-Peer Social Networks
• Statistical properties of sampled networks by random walks
• Immunization of Real Complex Communication Networks
• The fractal/small-world dichotomy in real-world networks
• Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices
• The effect of the forget-remember mechanism on spreading
• Fitness for Synchronization of Network Motifs
• Structural constraints in complex networks
• Network Structures from Selection Principles
• Ranking nodes in growing networks: When PageRank fails
• Percolation transition in networks with degree-degree correlation
• A Mutual Selection Model for Weighted Networks
• An efficient approach of controlling traffic congestion in scale-free networks
• Cyclic Topology in Complex Networks
• Efficient routing strategies in scale-free networks with limited bandwidth
• Zero Pearson Coefficient for Strongly Correlated Growing Trees
• Screened non-bonded interactions in native proteins manipulate optimal paths for robust residue communication
• A general geometric growth model for pseudofractal scale-free web
• Social cohesion, structural holes, and a tale of two measures
• Epidemic Threshold of an SIS Model in Dynamic Switching Networks
• Competition and adaptation in an Internet evolution model
• Loops structure of the Internet at the Autonomous System Level
• Spreading of infectious diseases on heterogeneous populations: multi-type network approach
• Computational complexity arising from degree correlations in networks
• The role of clustering and gridlike ordering in epidemic spreading
• Random Sierpinski network with scale-free small-world and modular structure
• Degree correlations in directed scale-free networks
• The Social Network of Contemporary Popular Musicians
• Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights
• A critical look at power law modelling of the Internet
• Griffiths phases and localization in hierarchical modular networks
• Comment on: 'Universal Behavior of Load Distribution in Scale-free Networks'
• Correlations in Bipartite Collaboration Networks
• Mapping Koch curves into scale-free small-world networks
• Dynamical evolution of clustering in complex network of earthquakes
• Intrinsic degree-correlations in static model of scale-free networks
• Degree Correlation in Scale-Free Graphs
• Understanding the internet topology evolution dynamics
• On the basic computational structure of gene regulatory networks
• Preferential attachment in growing spatial networks
• Accelerating, hyper-accelerating, and decelerating probabilistic networks
• Degree-dependent intervertex separation in complex networks
• Steady-State Dynamics of the Forest Fire Model on Complex Networks
• A Radar for the Internet
• Effect of node deleting on network structure
• Correlations in random Apollonian network
• Optimization of synchronization in gradient clustered networks
• Statistical significance of rich-club phenomena in complex networks
• Topologies and Laplacian spectra of a deterministic uniform recursive tree
• Statistical Self-Similar Properties of Complex Networks
• Analytical results for bond percolation and k-core sizes on clustered networks
• Network Formation Games with Heterogeneous Players and the Internet Structure
• The inhomogeneous evolution of subgraphs and cycles in complex networks
• On the topology of the world exchange arrangements web
• Griffiths phases in infinite-dimensional, non-hierarchical modular networks
• Power Grid Network Evolutions for Local Energy Trading
• Non massive immunization to contain spreading on complex networks
• Halting SARS-CoV-2 by Targeting High-Contact Individuals
• Cascades on clique-based graphs
• Generating random networks with given degree-degree correlations and degree-dependent clustering
• The Fractional Preferential Attachment Scale-Free Network Model
• Growing networks under geographical constraints
• Schroedinger-like PageRank equation and localization in the WWW
• Recursive weighted treelike networks
• Clustering Spectrum of scale-free networks
• The effects of degree correlations on network topologies and robustness
• Deterministic weighted scale-free small-world networks
• Hyperbolic Geometric Graph Representation Learning for Hierarchy-imbalance Node Classification
• Scale-free networks embedded in fractal space
• Assortative Mixing in Close-Packed Spatial Networks
• Variational principle for scale-free network motifs
• Measuring the Hierarchy of Feedforward Networks
• Power-law relations in random networks with communities
• Triadic closure in configuration models with unbounded degree fluctuations
• Parallel Generation of Massive Scale-Free Graphs
• Enhancing Robustness and Immunization in geographical networks
• Topological fractal networks introduced by mixed degree distribution
• Percolation and Loop Statistics in Complex Networks
• Node mixing and group structure of complex software networks
• Entropy-based randomisation of rating networks
• Master-equation analysis of accelerating networks
• Diffusion-annihilation proecesses in weighted scale-free networks with identical degree sequence
• Multilayer network analysis to study complex inter-subsystem interactions in a turbulent thermoacoustic system
• Flexible construction of hierarchical scale-free networks with general exponent
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• Subgraphs in preferential attachment models
• Dynamic Computation of Network Statistics via Updating Schema
• A General Stochastic Information Diffusion Model in Social Networks based on Epidemic Diseases
• User-Relatedness and Community Structure in Social Interaction Networks
• Scale-free network clustering in hyperbolic and other random graphs
• Counting triangles in power-law uniform random graphs
• Contact graphs of disk packings as a model of spatial planar networks
• Michaelis-Menten Dynamics in Complex Heterogeneous Networks
• Fundamental Structural Constraint of Random Scale-Free Networks
• Degree distribution and scaling in the Connecting Nearest Neighbors model
• Critical field-exponents for secure message-passing in modular networks
• Damage detection via shortest path network sampling
• Hamiltonian Dynamics of Preferential Attachment
• The Graph Structure of the Internet at the Autonomous Systems Level during Ten Years
• Generalized network community detection
• Enhancing synchronization in growing networks
• Heterogeneous Susceptibilities in Social Influence Models
• Structure constrained by metadata in networks of chess players
• Mechanism for linear preferential attachment in growing networks
• Susceptible-Infected-Recovered model on Euclidean network
• Scaling of the clustering function in spatial inhomogeneous random graphs
• Statistical physics of exchangeable sparse simple networks, multiplex networks and simplicial complexes
• The network asymmetry caused by the degree correlation and its effect on the bimodality in control
• Statistical Characteristics and Community analysis of Urban Road Networks
• Degree correlations in scale-free null models
• Clustering Coefficients of Protein-Protein Interaction Networks
• Internet data packet transport: from global topology to local queueing dynamics
• The behavior of rich-club coefficient in scale-free networks
• Influence of individual nodes for continuous-time Susceptible-Infected-Susceptible dynamics on synthetic and real-world networks
• Network heterogeneity and node capacity lead to heterogeneous scaling of fluctuations in random walks on graphs
• Fluctuation-induced traffic congestion in heterogeneous networks
• Describing and Simulating Internet Routes
• Efficient Network Generation Under General Preferential Attachment
• A Social Network Analysis of Articles on Social Network Analysis
• Quantum Motif Clustering
• Reconstruction of evolved dynamic networks from degree correlations
• Topological measures for the analysis of wireless sensor networks
• A Network Epidemic Model for Online Community Commissioning Data
• Co-evolution of networks and quantum dynamics: a generalization of preferential attachment
• Raising Graphs From Randomness to Reveal Information Networks
• From the Grid to the Smart Grid, Topologically
• Link-Space and Network Analysis
• On The Critical Packet Injection Rate Of A Preferential Next-Nearest Neighbor Routing Traffic Model On Barabasi-Albert Networks
• The Multiple Instances of Node Centrality and their Implications on the Vulnerability of ISP Networks
• Sharpest possible clustering bounds using robust random graph analysis
• Research on Life Characteristics of Internet Based on Network Motifs
• Synchronization of an evolving complex hyper-network
• Robust subgraph counting with distribution-free random graph analysis
• Adding Geographical Embedding to AS Topology Generation
• Analysis of a Model for Generating Weakly Scale-free Networks
• Earthquake Networks, Complex
• Generalized individual-based epidemic model for vulnerability assessment of correlated scale-free complex networks
• Finding induced subgraphs in scale-free inhomogeneous random graphs
• Strategic Formation of Heterogeneous Networks
• Identification of Key Companies for International Profit Shifting in the Global Ownership Network
• A New Benchmark For Evaluation Of Graph-Theoretic Algorithms