The diameter of the world wide web

Abstract

Despite its increasing role in communication, the world wide web remains the least controlled medium: any individual or institution can create websites with unrestricted number of documents and links. While great efforts are made to map and characterize the Internet's infrastructure, little is known about the topology of the web. Here we take a first step to fill this gap: we use local connectivity measurements to construct a topological model of the world wide web, allowing us to explore and characterize its large scale properties.

5 pages, 1 figure, updated with most recent results on the size of the www

Cited by in corpus (699)

• Emergence of scaling in random networks
• Fast unfolding of communities in large networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Community structure in social and biological networks
• Finding and evaluating community structure in networks
• Community detection in graphs
• Finding community structure in very large networks
• Error and attack tolerance of complex networks
• Epidemic spreading in scale-free networks
• Efficient Behavior of Small-World Networks
• Assortative mixing in networks
• The structure of scientific collaboration networks
• The large-scale organization of metabolic networks
• Random graphs with arbitrary degree distributions and their applications
• Near linear time algorithm to detect community structures in large-scale networks
• The spread of epidemic disease on networks
• Evolution of networks
• Mixing patterns in networks
• Classes of behavior of small-world networks
• Who is the best connected scientist? A study of scientific coauthorship networks
• Network robustness and fragility: Percolation on random graphs
• Spatial Networks
• Characterization of complex networks: A survey of measurements
• Defining and identifying communities in networks
• Resilience of the Internet to random breakdowns
• Critical phenomena in complex networks
• Community detection algorithms: a comparative analysis
• Hierarchical Organization in Complex Networks
• Clustering and preferential attachment in growing networks
• Attack vulnerability of complex networks
• Community detection in networks: A user guide
• Epidemic dynamics and endemic states in complex networks
• Self-similarity of complex networks
• Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
• Topology of evolving networks: local events and universality
• Higher-order organization of complex networks
• Immunization of complex networks
• Subgraph Centrality in Complex Networks
• Universal Behavior of Load Distribution in Scale-free Networks
• Growing Scale-Free Networks with Tunable Clustering
• Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities
• A tool for filtering information in complex systems
• Scale-free networks are rare
• Organization of Growing Random Networks
• Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
• Scale-Free Networks are Ultrasmall
• Bose-Einstein condensation in complex networks
• Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications
• Evolutionary games on multilayer networks: A colloquium
• Kronecker Graphs: An Approach to Modeling Networks
• Activity driven modeling of time varying networks
• Problems with Fitting to the Power-Law Distribution
• Epidemic dynamics in finite size scale-free networks
• Betweenness Centrality in Large Complex Networks
• Topology of the World Trade Web
• First-passage times in complex scale-invariant media
• Origins of fractality in the growth of complex networks
• Optimal network topologies for local search with congestion
• Clustering and Community Detection in Directed Networks: A Survey
• Small-world properties of the Indian Railway network
• Measuring preferential attachment for evolving networks
• Exact Controllability of Complex Networks
• Emergence of network features from multiplexity
• Growing networks with local rules: preferential attachment, clustering hierarchy and degree correlations
• Mixture models and exploratory analysis in networks
• The phase transition in inhomogeneous random graphs
• Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
• Properties of highly clustered networks
• Efficiency of Scale-Free Networks: Error and Attack Tolerance
• Statistical Analysis of Airport Network of China
• Patterns of link reciprocity in directed networks
• Weighted Evolving Networks
• Deterministic Scale-Free Networks
• Topology of correlation based minimal spanning trees in real and model markets
• Software systems as complex networks: structure, function, and evolvability of software collaboration graphs
• Class of correlated random networks with hidden variables
• Are randomly grown graphs really random?
• Evolution of reference networks with aging
• Synchronization on small-world networks
• Controlling edge dynamics in complex networks
• Layered Complex Networks
• Networks of equities in financial markets
• A Tutorial in Connectome Analysis: Topological and Spatial Features of Brain Networks
• Classification of scale-free networks
• Analysis of a large-scale weighted network of one-to-one human communication
• Growing Scale-Free Networks with Small World Behavior
• Growing multiplex networks
• Complex Networks as Hypergraphs
• Betweenness centrality correlation in social networks
• Generic scale of the "scale-free" growing networks
• Giant strongly connected component of directed networks
• Bipartite Graphs as Models of Complex Networks
• Global Organization of the Lexicon
• Modelling the Air Transport with Complex Networks: a short review
• Graph Metrics for Temporal Networks
• Triadic closure as a basic generating mechanism of communities in complex networks
• Maximal planar networks with large clustering coefficient and power-law degree distribution
• Self-organization of collaboration networks
• Edge direction and the structure of networks
• Scaling properties of scale-free evolving networks: Continuous approach
• Core-periphery organization of complex networks
• Characterizing and modeling the dynamics of online popularity
• Hierarchical Block Structures and High-resolution Model Selection in Large Networks
• Scaling Behaviour of Developing and Decaying Networks
• General Dynamics of Topology and Traffic on Weighted Technological Networks
• Factors that predict better synchronizability on complex networks
• Understanding the Characteristics of Internet Short Video Sharing: YouTube as a Case Study
• Spectra and eigenvectors of scale-free networks
• Skeleton and fractal scaling in complex networks
• Instability of scale-free networks under node-breaking avalanches
• Vertex overload breakdown in evolving networks
• Network resilience
• Emergence of bimodality in controlling complex networks
• Preferential attachment in the protein network evolution
• Truncation of power law behavior in "scale-free" network models due to information filtering
• Crawling Facebook for Social Network Analysis Purposes
• Epidemic spread in weighted scale-free networks
• Efficiency of informational transfer in regular and complex networks
• Edge overload breakdown in evolving networks
• Effect of the accelerating growth of communications networks on their structure
• The clustering coefficient and community structure of bipartite networks
• Understanding the spreading power of all nodes in a network: a continuous-time perspective
• Correlation based networks of equity returns sampled at different time horizons
• Unfolding communities in large complex networks: Combining defensive and offensive label propagation for core extraction
• Scaling laws for the movement of people between locations in a large city
• The network topology of a potential energy landscape: A static scale-free network
• Entropy Rate of Diffusion Processes on Complex Networks
• Global mean first-passage times of random walks on complex networks
• Dynamical properties of model communication networks
• Exact solutions for models of evolving networks with addition and deletion of nodes
• A Geometric Fractal Growth Model for Scale Free Networks
• The Fractal Properties of Internet
• Designing optimal transport networks
• Citation Networks in High Energy Physics
• Sparse graphs using exchangeable random measures
• Path finding strategies in scale-free networks
• Ising model in small-world networks
• Human dynamics revealed through Web analytics
• Efficient modularity optimization by multistep greedy algorithm and vertex mover refinement
• Detecting criminal organizations in mobile phone networks
• Local modularity measure for network clusterizations
• Small world-Fractal Transition in Complex Networks: Renormalization Group Approach
• First passage time for random walks in heterogeneous networks
• Identifying "communities" within energy landscapes
• Multiplicative Attribute Graph Model of Real-World Networks
• All scale-free networks are sparse
• Exploring complex networks by walking on them
• Hierarchical Small Worlds in Software Architecture
• Structure of a large social network
• Self-similar disk packings as model spatial scale-free networks
• The Large Scale Curvature of Networks
• The Rise of Network Ecology: Maps of the topic diversity and scientific collaboration
• Methods for estimating the size of Google Scholar
• Nonequilibrium Phase Transitions in Directed Small-World Networks
• Spanning Trees and bootstrap reliability estimation in correlation based networks
• Fractality in complex networks: critical and supercritical skeletons
• Separating internal and external dynamics of complex systems
• The egalitarian effect of search engines
• Modulated Scale-free Network in the Euclidean Space
• Models of the Small World: A Review
• Anomalous percolating properties of growing networks
• Compact Routing on Internet-Like Graphs
• Backbone of complex networks of corporations: The flow of control
• Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management
• Multi-scale community organization of the human structural connectome and its relationship with resting-state functional connectivity
• Growing Random Networks with Fitness
• Weighted Assortative And Disassortative Networks Model
• XY model in small-world networks
• Scale-free trees: the skeletons of complex networks
• Distinct types of eigenvector localization in networks
• Structural transitions in scale-free networks
• Scale-Free Networks Generated By Random Walkers
• Strong correlations between text quality and complex networks features
• Multiscale mixing patterns in networks
• Fastest learning in small world neural networks
• Signatures of small-world and scale-free properties in large computer programs
• Model selection and hypothesis testing for large-scale network models with overlapping groups
• Rate equation approach for correlations in growing network models
• Characteristics of the Korean stock market correlations
• Cascading Dynamics in Modular Networks
• Evolving networks with disadvantaged long-range connections
• Preferential attachment growth model and nonextensive statistical mechanics
• Recursive graphs with small-world scale-free properties
• Evolving Clustered Random Networks
• Heterogeneous Bond Percolation on Multitype Networks with an Application to Epidemic Dynamics
• Evolutionary reconstruction of networks
• Centrality Measures for Networks with Community Structure
• Self-similar scaling of density in complex real-world networks
• Growth and structure of Slovenia's scientific collaboration network
• Scale-free Network in Financial Correlations
• Small-World Networks: Links with long-tailed distributions
• Exactly solvable analogy of small-world networks
• Component sizes in networks with arbitrary degree distributions
• Small-world networks and the conformation space of a lattice polymer chain
• Information filtering in complex weighted networks
• Opinion and community formation in coevolving networks
• Characteristic times of biased random walks on complex networks
• Hierarchical characterization of complex networks
• Functional Integration of Ecological Networks through Pathway Proliferation
• A box-covering algorithm for fractal scaling in scale-free networks
• Topology and correlations in structured scale-free networks
• Quantum Google in a Complex Network
• Entanglement percolation in quantum complex networks
• Immunization of networks with community structure
• The large-scale structure of semantic networks: statistical analyses and a model for semantic growth
• Characterizing the network topology of the energy landscapes of atomic clusters
• Travel and tourism: Into a complex network
• How humans learn and represent networks
• Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks
• Structural properties of spatially embedded networks
• Community Detecting By Signaling on Complex Networks
• A New Comparative Definition of Community and Corresponding Identifying Algorithm
• On the rich-club effect in dense and weighted networks
• Extreme self-organization in networks constructed from gene expression data
• A Walk in Facebook: Uniform Sampling of Users in Online Social Networks
• First- and second-order phase transitions in scale-free networks
• High dimensional random Apollonian networks
• Weighted Scale-Free Networks with Stochastic Weight Assignments
• Recent advances of percolation theory in complex networks
• Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation
• Ising model in scale-free networks: A Monte Carlo simulation
• Network Community Detection: A Review and Visual Survey
• Higher order clustering coefficients in Barabasi-Albert networks
• Non-linear growth and condensation in multiplex networks
• Statistical properties of sampled networks by random walks
• Bicomponents and the robustness of networks to failure
• The fractal/small-world dichotomy in real-world networks
• Quarantine generated phase transition in epidemic spreading
• Inducing Effect on the Percolation Transition in Complex Networks
• Deterministic Small-World Networks
• The network of concepts in written texts
• Navigating the massive world of reddit: Using backbone networks to map user interests in social media
• Self-avoiding walks on scale-free networks
• Social inertia in collaboration networks
• The spread of disease with birth and death on networks
• Wiring cost in the organization of a biological network
• Asymptotic behavior and distributional limits of preferential attachment graphs
• Cyclic Topology in Complex Networks
• An efficient approach of controlling traffic congestion in scale-free networks
• A Mutual Selection Model for Weighted Networks
• The structural role of weak and strong links in a financial market network
• Persistence in Complex Systems
• Spectral Characteristics of Network Redundancy
• Phase transition in a directed traffic flow network
• Synchronized clusters in coupled map networks: Self-organized and driven phase synchronization
• Competitive cluster growth in complex networks
• Exact scaling properties of a hierarchical network model
• Random walk and trapping processes on scale-free networks
• On fitting the Pareto-Levy distribution to stock market index data: selecting a suitable cutoff value
• Trapping in complex networks
• Inter-Package Dependency Networks in Open-Source Software
• The h-Index of a Graph and its Application to Dynamic Subgraph Statistics
• Quantifying the connectivity of a network: The network correlation function method
• Multifractality of complex networks
• Statistical properties of the quantum internet
• Multistep greedy algorithm identifies community structure in real-world and computer-generated networks
• Download relaxation dynamics on the WWW following newspaper publication of URL
• Perturbation: the Catastrophe Causer in Scale-Free Networks
• The role of clustering and gridlike ordering in epidemic spreading
• Assessing the direction of climate interactions by means of complex networks and information theoretic tools
• Scale-free networks with exponent one
• Urban traffic from the perspective of dual graph
• Multiscale characterization of recurrence-based phase space networks constructed from time series
• Bipartite Producer-Consumer Networks and the Size Distribution of Firms
• Random Sierpinski network with scale-free small-world and modular structure
• Statistics of Cycles: How Loopy is your Network?
• Generation of arbitrarily two-point correlated random networks
• Stochastic Opinion Formation in Scale-Free Networks
• Emergence of Symmetry in Complex Networks
• Adaptive financial networks with static and dynamic thresholds
• Universal fractal scaling of self-organized networks
• Scale free networks from a Hamiltonian dynamics
• Degree correlations in directed scale-free networks
• Epidemic Dynamics of Interacting Two Particle Species on Scale-free Networks
• Exact results and scaling properties of small-world networks
• Understanding cancer complexome using networks, spectral graph theory and multilayer framework
• Random Walks on Directed Networks: the Case of PageRank
• Fractional Dynamics of Network Growth Constrained by aging Node Interactions
• A complex network approach to robustness and vulnerability of spatially organized water distribution networks
• Giant Clusters in Random Ad Hoc Networks
• The diameter of sparse random graphs
• The Phase Stability Network of all Inorganic Materials
• Scaling of random spreading in small world networks
• Self Organized Scale-Free Networks from Merging and Regeneration
• Statistical Analysis of Bus Networks in India
• Modeling Dynamics of Information Networks
• Universality of the transverse momentum distributions in the framework of percolation of strings
• The effect of bandwidth in scale-free network traffic
• Multifractal analysis of complex networks
• Degree Distribution in Quantum Walks on Complex Networks
• Ising-like agent-based technology diffusion model: adoption patterns vs. seeding strategies
• Correlations in connected random graphs
• A Mutual Attraction Model for Both Assortative and Disassortative Weighted Networks
• Bug propagation and debugging in asymmetric software structures
• The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks
• Enhanced Flow in Small-World Networks
• Frequency of occurrence of numbers in the World Wide Web
• Satellite-based photonic quantum networks are small-world
• Controllability and maximum matchings of complex networks
• On the Complexity of Newman's Community Finding Approach for Biological and Social Networks
• Exactly solvable scale-free network model
• Response time of internauts
• Explosion in weighted Hyperbolic Random Graphs and Geometric Inhomogeneous Random Graphs
• A general model for collaboration networks
• Growing network model for community with group structure
• How to fit the degree distribution of the air network?
• The Bak-Sneppen Model on Scale-Free Networks
• Efficient network immunization under limited knowledge
• Integer Networks
• Smallest small-world network
• Re-inventing Willis
• Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters
• Energy cost for controlling complex networks
• Evolution of the digital society reveals balance between viral and mass media influence
• Complex networks embedded in space: Dimension and scaling relations between mass, topological distance and Euclidean distance
• Homogeneous temporal activity patterns in a large online communication space
• Finding network communities using modularity density
• Mapping Out Narrative Structures and Dynamics Using Networks and Textual Information
• Degree-dependent intervertex separation in complex networks
• Modeling the average shortest path length in growth of word-adjacency networks
• Degree distributions of bipartite networks and their projections
• A steady state model for graph power laws
• Influence of reciprocal arcs on the degree distribution and degree correlations
• Bridges in Complex Networks
• Extremal-point Densities of Interface Fluctuations
• Fast Exact Shortest-Path Distance Queries on Large Networks by Pruned Landmark Labeling
• Limited path entanglement percolation in quantum complex networks
• On the distribution of career longevity and the evolution of home run prowess in professional baseball
• Accuracy Test for Link Prediction in terms of Similarity Index: The Case of WS and BA Models
• Local clustering in scale-free networks with hidden variables
• A directed network model for World-Wide Web
• Growing Trees in Internet News Groups and Forums
• Graph Neural Networks: Methods, Applications, and Opportunities
• Families and clustering in a natural numbers network
• Diffusion in scale-free networks with annealed disorder
• Impact of hierarchical modular structure on ranking of individual nodes in directed networks
• Preferencial growth: exact solution of the time dependent distributions
• Self-avoiding walks and connective constants in small-world networks
• Local-world evolving networks with tunable clustering
• Statistical Self-Similar Properties of Complex Networks
• Phase ordering on small-world networks with nearest-neighbor edges
• Functional centrality in graphs
• Links tell us about lexical and semantic Web content
• Renormalization flows in complex networks
• Analytical results for bond percolation and k-core sizes on clustered networks
• Multifractal properties of growing networks
• Information flow networks of Chinese stock market sectors
• Synchronization Landscapes in Small-World-Connected Computer Networks
• On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia
• Stability of complex networks under the evolution of attack and repair
• Constrained spin dynamics description of random walks on hierarchical scale-free networks
• Quantum and classical diffusion in small-world networks
• SIS Epidemic Spreading with Correlated Heterogeneous Infection Rates
• Universality at Breakdown of Quantum Transport on Complex Networks
• Deterministic hierarchical networks
• Growing Scale-free Networks by a Mediation-Driven Attachment Rule
• Degree Distribution, Rank-size Distribution, and Leadership Persistence in Mediation-Driven Attachment Networks
• Testing a priority-based queue model with Linux command histories
• Empirical study on clique-degree distribution of networks
• Ising model in clustered scale-free networks
• Power Grid Network Evolutions for Local Energy Trading
• Correlations in Scale-Free Networks: Tomography and Percolation
• Diffusive Capture Process on Complex Networks
• Sampling properties of directed networks
• Spreading of Persistent Infections in Heterogeneous Populations
• Recursive weighted treelike networks
• The Fractional Preferential Attachment Scale-Free Network Model
• Identifying overlapping communities in social networks using multi-scale local information expansion
• Measuring Fundamental Properties of Real-World Complex Networks
• A preferential attachment model with Poisson growth for scale-free networks
• Input graph: the hidden geometry in controlling complex networks
• Chain motifs: The tails and handles of complex networks
• Multifractality and Laplace spectrum of horizontal visibility graphs constructed from fractional Brownian motions
• Clustering Spectrum of scale-free networks
• Spin glass behavior of the antiferromagnetic Ising model on a scale-free network
• Contagion spreading on complex networks with local deterministic dynamics
• Evolution of Vocabulary on Scale-free and Random Networks
• Pre-train and Learn: Preserve Global Information for Graph Neural Networks
• Topological structure and the H-index in complex networks
• The small-world effect is a modern phenomenon
• FastSIR Algorithm: A Fast Algorithm for simulation of epidemic spread in large networks by using SIR compartment model
• Detrending career statistics in professional baseball: Accounting for the steroids era and beyond
• A Game Theoretical Approach to Modeling Information Dissemination in Social Networks
• A network approach for the scientific collaboration in the European Framework Programs
• Scale-free download network for publications
• Hypersparse Neural Network Analysis of Large-Scale Internet Traffic
• Characteristics of Real Futures Trading Networks
• The Anderson-Darling test of fit for the power law distribution from left censored samples
• Dense networks with scale-free feature
• Maximum flow and topological structure of complex networks
• Scaling theory of fractal complex networks
• Social inertia and diversity in collaboration networks
• Universal Scaling Behavior of Clustering Coefficient Induced by Deactivation Mechanism
• A simple model clarifies the complicated relationships of complex networks
• Effect of size heterogeneity on community identification in complex networks
• Neuropsychological constraints to human data production on a global scale
• Ant Colony Optimization with a New Random Walk Model for Community Detection in Complex Networks
• Agent-Based Simulations of Blockchain protocols illustrated via Kadena's Chainweb
• Analytical results for stochastically growing networks: connection to the zero range process
• A Generalized and Adaptive Method for Community Detection
• Impact of perception models on friendship paradox and opinion formation
• Social Network Analysis Taxonomy Based on Graph Representation
• Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks
• Random spreading phenomena in annealed small world networks
• Extended h-Index Parameterized Data Structures for Computing Dynamic Subgraph Statistics
• Long-Range Connections in Transportation Networks
• Variational principle for scale-free network motifs
• Identifying time dependence in network growth
• Power-law distributions from additive preferential redistributions
• Network Analysis of Cosmic Structures : Network Centrality and Topological Environment
• Optimal random search for a single hidden target
• Introducing Small-World Network Effect to Critical Dynamics
• Intentional Walks on Scale Free Small Worlds
• Preferential attachment during the evolution of a potential energy landscape
• Scaling behavior of an artificial traffic model on scale-free networks
• Growing dynamics of Internet providers
• Same Stats, Different Graphs: Exploring the Space of Graphs in Terms of Graph Properties
• Link and subgraph likelihoods in random undirected networks with fixed and partially fixed degree sequence
• Time-Varying Graphs and Dynamic Networks
• Planting Trees for scalable and efficient Canonical Hub Labeling
• Power-law relations in random networks with communities
• Percolation of Hierarchical Networks and Networks of Networks
• Long and short paths in uniform random recursive dags
• Border trees of complex networks
• Spectral Statistics of Sparse Random Graphs with a General Degree Distribution
• Extracting directed information flow networks: an application to genetics and semantics
• Robustness of the in-degree exponent for the world-wide web
• Simple models of small world networks with directed links
• Dynamic scaling, data-collapse and self-similarity in Barabási-Albert networks
• Quasistatic Scale-free Networks
• Gutenberg-Richter Law for Internetquakes
• Triadic closure in configuration models with unbounded degree fluctuations
• A scale-free network hidden in the collapsing polymer
• Kinetic growth walks on complex networks
• Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks
• Correlations in interacting systems with a network topology
• Robustness of community structure to node removal
• Automatic Network Fingerprinting through Single-Node Motifs
• Degree difference: A simple measure to characterize structural heterogeneity in complex networks
• Effects of reciprocity on random walks in weighted networks
• Topological fractal networks introduced by mixed degree distribution
• Analysis of the convergence of the degree distribution of contracting random networks towards a Poisson distribution using the relative entropy
• ProtNN: Fast and Accurate Nearest Neighbor Protein Function Prediction based on Graph Embedding in Structural and Topological Space
• Spatial Temporal Analysis of 40,000,000,000,000 Internet Darkspace Packets
• Ordered community detection in directed networks
• Centrality Measures in Complex Networks: A Survey
• Convergence towards an Erd{\H o}s-Rényi graph structure in network contraction processes
• Scale-free network on a vertical plane
• Identifying a set of influential spreaders in complex networks
• Critical properties of a dissipative sandpile model on small world networks
• Antiferromagnetic Ising model in scale-free networks
• Modeling the topology of protein interaction networks
• Thermodynamic approach for community discovering within the complex networks: LiveJournal study
• Two-dimensional small-world networks: navigation with local information
• Evolving Twitter: an experimental analysis of graph properties of the social graph
• Multi-Temporal Analysis and Scaling Relations of 100,000,000,000 Network Packets
• Socio-economic inequalities: a statistical physics perspective
• Temporal and spatial evolution of the distribution related to the number of COVID-19 pandemic
• An analytically solvable model of probabilistic network dynamics
• Dissortativity and duplications in Oral cancer
• Unfolding network communities by combining defensive and offensive label propagation
• Elastic and inelastic transmission in guided atom lasers: a truncated Wigner approach
• Modelling opinion formation driven communities in social networks
• Kinetic-growth self-avoiding walks on small-world networks
• Statistical mechanics of coevolving spin system
• Heterogeneous message passing for heterogeneous networks
• Scale-free networks with tunable degree distribution exponents
• Enhancing Transport Efficiency by Hybrid Routing Strategy
• An optimal network for passenger traffic
• Fragmenting networks by targeting collective influencers at a mesoscopic level
• Hashkat: Large-scale simulations of online social networks
• Scale-free network clustering in hyperbolic and other random graphs
• Reciprocity in directed networks
• Network analysis of 3D complex plasma clusters in a rotating electric field
• Explosion and distances in scale-free percolation
• A self-consistent approach to measure preferential attachment in networks and its application to an inherent structure network
• Benefits of Semantics on Web Service Composition from a Complex Network Perspective
• Fundamental Structural Constraint of Random Scale-Free Networks
• Complex systems: features, similarity and connectivity
• A small-world search for quantum speedup: How small-world interactions can lead to improved quantum annealer designs
• Scale-Free model for governing universe dynamics
• Transitions in spatial networks
• Evolution of diversity and dominance of companies in online activity
• Dynamical Complex Network Models of the Turbulent Cascade
• Sandpile model on an optimized scale-free network on Euclidean space
• Self-avoiding walks and connective constants in clustered scale-free networks
• Size of quantum networks
• Modeling interacting dynamic networks: II. Systematic study of the statistical properties of cross-links between two networks with preferred degrees
• The Cover Time of Random Walks on Graphs
• Vertex labeling and routing in expanded Apollonian networks
• Efficient priority queueing routing strategy on mobile networks
• The Power Grid as a Complex Network: a Survey
• Properties of weighted complex networks
• Dismantling Efficiency and Network Fractality
• Statistical Investigation of Avalanches of Three Dimensional Small-World Networks and their Boundary and Bulk Cross-Sections
• Two faces of greedy leaf removal procedure on graphs
• Weighted distances in scale-free preferential attachment models
• Preferential growth: Solution and application to modeling stock market
• Heavy-tailed distributions of confirmed COVID-19 cases and deaths in spatiotemporal space
• Quantum Chaos in Random Ising Networks
• Generation of scale-free networks using a simple preferential rewiring dynamics
• Mechanism for linear preferential attachment in growing networks
• Crafting networks to achieve, or not achieve, chaotic states
• Phase diagram of epidemic spreading - unimodal vs. bimodal probability distributions
• Hybrid Power-Law Models of Network Traffic
• Sparse power-law network model for reliable statistical predictions based on sampled data
• Random Processes with High Variance Produce Scale Free Networks
• Spacing ratio statistics of multiplex directed networks
• Impact of random and targeted disruptions on information diffusion during outbreaks
• Graph Theory and Networks in Biology
• Structure of international trade hypergraphs
• Bootstrap percolation in directed and inhomogeneous random graphs
• Complex networks with scale-free nature and hierarchical modularity
• Modelling Selforganization and Innovation Processes in Networks
• Hyperparameter-free and Explainable Whole Graph Embedding
• Decoding the structure of the WWW: facts versus sampling biases
• Altering nodes types in controlling complex networks
• Learning from User Interactions with Rankings: A Unification of the Field
• Why are probabilistic laws governing quantum mechanics and neurobiology?
• Sznajd Complex Networks
• Empirical comparison of network sampling techniques
• Nodal domain partition and the number of communities in networks
• Giant component sizes in scale-free networks with power-law degrees and cutoffs
• Criterions for locally dense subgraphs
• Communities in C.elegans connectome through the prism of non-backtracking walks
• Power laws of the in-degree and out-degree distributions of complex networks
• Arrow Matrix Decomposition: A Novel Approach for Communication-Efficient Sparse Matrix Multiplication
• Steady States of Epidemic Spreading in Small-World Networks
• Growing random networks under constraints
• Segregation in the annihilation of two-species reaction-diffusion processes on fractal scale-free networks
• Universal features of mountain ridge networks on Earth
• Cycle-centrality in complex networks
• Degree correlations in scale-free null models
• Obtaining Communities with a Fitness Growth Process
• Theoretical approach and impact of correlations on the critical packet generation rate in traffic dynamics on complex networks
• The origin of preferential attachment and the generalized preferential attachment for weighted networks
• Explaining the stellar initial mass function with the theory of spatial networks
• Fermionic Networks: Modeling Adaptive Complex Networks with Fermionic Gases
• Filtering of complex systems using overlapping tree networks
• Stochastic model for scale-free networks with cutoffs
• Growing Networks: Limit in-degree distribution for arbitrary out-degree one
• On the Degree Sequence and its Critical Phenomenon of an Evolving Random Graph Process
• Quantum phase transition of the transverse-field quantum Ising model on scale-free networks
• Clustering Algorithms for Scale-free Networks and Applications to Cloud Resource Management
• Web Services Dependency Networks Analysis
• Unifying Evolutionary and Network Dynamics
• Emergence of scale-free properties in Hebbian networks
• Canonical fitness model for simple scale-free graphs
• Near Optimal Routing for Small-World Networks with Augmented Local Awareness
• A scalable method to find the shortest path in a graph with circuits of memristors
• Temporal Correlation of Internet Observatories and Outposts
• A transition from river networks to scale-free networks
• Giant component in a configuration-model power-law graph with a variable number of links
• Boolean decision problems with competing interactions on scale-free networks: Critical thermodynamics
• Distance Distribution in Extreme Modular Networks
• Multifractality of complex networks is also due to geometry. The Geometric SandBox algorithm
• From Random Graph to Small World by Wandering
• Exact solutions of epidemic models on networks
• Degree distributions in networks: beyond the power law
• Generating multi-scaling networks with different types of nodes
• Robustness of Random Networks with Selective Reinforcement against Attacks
• Near-optimal adjacency labeling scheme for power-law graphs
• Diffusion limited friendship network: A model for six degrees of separation
• Scale-free networks are not robust under neutral evolution
• Dynamic Scaling, Data-collapse and Self-Similarity in Mediation-Driven Attachment Networks
• Disassortativity of random critical branching trees
• The clash of the Titans: how preferential attachment helps the survival of the smallest
• Bifractality of fractal scale-free networks
• Correlation effects in a simple model of small-world network
• Evolving complex networks with conserved clique distributions
• Correlation networks from random walk time series
• Network Science approach to Modelling Emergence and Topological Robustness of Supply Networks: A Review and Perspective
• Comparing the sensitivity of social networks, web graphs, and random graphs with respect to vertex removal
• Properties of Latent Variable Network Models
• Parenclitic networks: a multilayer description of heterogeneous and static data-sets
• A large-scale study of the World Wide Web: network correlation functions with scale-invariant boundaries
• A weighted planar stochastic lattice with scale-free, small-world and multifractal properties
• Synchronization in Small-World-Connected Computer Networks
• Inhomogeneous substructures hidden in random networks
• Principles in the Evolution of Metabolic Networks
• Eigenvalue Preferential Attachment Networks A Dandelion Structure
• Self-organized network design by link survivals and shortcuts
• Error-correcting codes on scale-free networks
• Quantum Motif Clustering
• The idemetric property: when most distances are (almost) the same
• Network analysis with quantum dynamics clarifies why photosystem II exploits both chlorophyll a and b
• On the Capacity of Fractal D2D Social Networks with Hierarchical Communications
• Analytic Solution to Clustering Coefficients on Weighted Networks
• Boolean decision problems with competing interactions on scale-free networks: Equilibrium and nonequilibrium behavior in an external bias
• Dynamics of disease spread. Effect of the characteristic times
• Towards Limited Scale-free Topology with Dynamic Peer Participation
• The Degree Sequence of a Scale-Free Random Graph Process with Hard Copying
• A Network Epidemic Model for Online Community Commissioning Data
• Gaussian Networks Generated by Random Walks
• Efficiency of message transmission using biased random walks in complex networks in the presence of traps
• Ranking pages and the topology of the web
• Network Extreme Eigenvalue - from Multimodal to Scale-free Network
• Modules of human micro-RNA co-target network
• Optimal box-covering algorithm for fractal dimension of complex networks
• Conformation-networks of two-dimensional lattice homopolymers
• Weighted scale-free network with self-organizing link weight dynamics
• The network structure of mathematical knowledge according to the Wikipedia, MathWorld, and DLMF online libraries
• Power Law of Customers' Expenditures in Convenience Stores
• A subset selection based approach to finding important structure of complex networks
• A Social Network Analysis of Articles on Social Network Analysis
• Novel Adaptive Algorithms for Estimating Betweenness, Coverage and k-path Centralities
• Efficient Network Generation Under General Preferential Attachment
• Interpretations of the Web of Data
• Teaching Network Traffic Matrices in an Interactive Game Environment
• What is Normal? A Big Data Observational Science Model of Anonymized Internet Traffic
• A computational study explaining processes underlying phase transition
• Nonequilibrium phase transitions in a racism-spreading model with interaction-driven dynamics
• Ad-hoc Limited Scale-Free Models for Unstructured Peer-to-Peer Networks
• Big data need physical ideas and methods
• Scaling exponents and phase separation in a nonlinear network model inspired by the gravitational accretion
• On The Critical Packet Injection Rate Of A Preferential Next-Nearest Neighbor Routing Traffic Model On Barabasi-Albert Networks
• A Simple Model of Scale-free Networks Driven by both Randomness and Adaptability
• Transforming Graph Representations for Statistical Relational Learning
• The darkweb: a social network anomaly
• Phase Transition on The Degree Sequence of a Mixed Random Graph Process
• Detrended fluctuation analysis on the correlations of complex networks under attack and repair strategy
• Emergence of Multivariate Extremes in Multilayer Inhomogeneous Random Graphs
• Computing the smallest eigenpairs of the graph Laplacian
• ReHub. Extending Hub Labels for Reverse k-Nearest Neighbor Queries on Large-Scale networks
• The Evolution of the Cuban HIV/AIDS Network
• Modified Lomax Model: A heavy-tailed distribution for fitting large-scale real-world complex networks
• Structure of multipartite entanglement in random cluster-like photonic systems
• Modelling Diffuse Subcellular Protein Structures as Dynamic Social Networks
• Betweenness Centrality as a Driver of Preferential Attachment in the Evolution of Research Collaboration Networks
• Hypernets -- Good (G)news for Gnutella
• Expected Message Delivery Time for Small-world Networks in the Continuum Limit
• A resource- and computationally-efficient protocol for multipartite entanglement distribution in Bell-pair networks
• An effective local routing strategy on the BA network
• How network properties and epidemic parameters influence stochastic SIR dynamics on scale-free random networks
• Scale-free percolation in continuum space: quenched degree and clustering coefficient
• On Sharing Viral Video over an Ad Hoc Wireless Network
• HIF: The hypergraph interchange format for higher-order networks
• On the Role of Triadic Substructures in Complex Networks
• Online Distributed Job Dispatching with Outdated and Partially-Observable Information
• Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics
• SocialFilter: Collaborative Spam Mitigation using Social Networks
• Combinatorial-Probabilistic Trade-Off: Community Properties Test in the Stochastic Block Models
• Modeling Information Diffusion in Social Networks
• Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States
• The Truth about Power Laws: Theory and Reality
• Same Stats, Different Graphs (Graph Statistics and Why We Need Graph Drawings)
• Scale-Free Overlay Topologies with Hard Cutoffs for Unstructured Peer-to-Peer Networks
• Modeling and Analysis of Cascading Failures in Interdependent Cyber-Physical Systems
• Social Ranking Techniques for the Web
• Harris-Luck criterion in the plateau transition of the Integer Quantum Hall Effect
• On the Value of a Social Network
• Emergence of correlations in highly biased Consensus Models in seed initial configuration
• A study on the performance of similarity indices and its relationship with link prediction: a two-state random network case
• Quantitative Graph Theory: A new branch of graph theory and in network science
• Bring your friend! Real or virtual?
• A Markov Chain-Based Numerical Method for Calculating Network Degree Distributions
• A new general family of deterministic hierarchical networks
• Discriminative Distance-Based Network Indices with Application to Link Prediction
• Robustness surfaces of complex networks
• Impact of Random Failures and Attacks on Poisson and Power-Law Random Networks
• Symbolic walk in regular networks
• Construction of Small Worlds in the Physical Topology of Wireless Networks
• R&D Strategy Document
• Generating constrained random graphs using multiple edge switches
• Spaceland Embedding of Sparse Stochastic Graphs
• Multi-Likelihood Methods for Developing Stock Relationship Networks Using Financial Big Data
• Reciprocity in Social Networks with Capacity Constraints
• Navigating the Small World Web by Textual Cues
• A class of randomized Subset Selection Methods for large complex networks
• Planet-scale Human Mobility Measurement
• Detection of network inhomogeneity by total neighbor degree
• Network topology transition at criticality
• Power-law distributions, the h-index, and Google Scholar (GS) citations: a test of their relationship with economics Nobelists
• Quantum walk inspired algorithm for graph similarity and isomorphism
• On the Approximability of Independent Set Problem on Power Law Graphs
• Quantum Google Algorithm: Construction and Application to Complex Networks
• Simulating the Influence of Collaborative Networks on the Structure of Networks of Organizations, Employment Structure, and Organization Value
• A Threshold For Clusters in Real-World Random Networks
• Identification of phases in scale-free networks
• Membership(s) and compliance(s) with class-based graphs
• Controlling network dynamics
• High Degree Vertices, Eigenvalues and Diameter of Random Apollonian Networks
• Analytical and numerical studies of creation probabilities of hierarchical trees
• SIR epidemics on a scale-free spatial nested modular network with a non-trivial threshold
• Random Walks on Complex Networks
• Finding induced subgraphs in scale-free inhomogeneous random graphs
• Robustness of soil ecosystems under different regimes of management
• Evanescent random walker on networks: Hitting times, budget renewal, and survival dynamics
• Birth-Burst in Evolving Networks
• Statistical properties of telephone communication network
• Nonreciprocal random networks and their percolation properties
• On the Heterogeneous Distributions in Paper Citations
• Complex network prediction using deep learning
• A systematic association of subgraph counts over a network
• Stability of the LCD Model
• On Topological Structure of Web Services Networks for Composition
• Italian Business-to-Business Invoicing Data: A Network Analysis
• Frequency-aware SGD for Efficient Embedding Learning with Provable Benefits