A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Network topology generators: degree-based vs. structural
Proceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications
BRITE: An Approach to Universal Topology Generation
MASCOTS '01 Proceedings of the Ninth International Symposium in Modeling, Analysis and Simulation of Computer and Telecommunication Systems
A first-principles approach to understanding the internet's router-level topology
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
The internet AS-level topology: three data sources and one definitive metric
ACM SIGCOMM Computer Communication Review
Evolution of Networks: From Biological Nets to the Internet and WWW (Physics)
Evolution of Networks: From Biological Nets to the Internet and WWW (Physics)
Efficient and simple generation of random simple connected graphs with prescribed degree sequence
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Binomial and Poisson distributions as maximum entropy distributions
IEEE Transactions on Information Theory
The workshop on internet topology (wit) report
ACM SIGCOMM Computer Communication Review
Decoding the structure of the WWW: A comparative analysis of Web crawls
ACM Transactions on the Web (TWEB)
Can ISPS and P2P users cooperate for improved performance?
ACM SIGCOMM Computer Communication Review
Observing the evolution of internet as topology
Proceedings of the 2007 conference on Applications, technologies, architectures, and protocols for computer communications
Orbis: rescaling degree correlations to generate annotated internet topologies
Proceedings of the 2007 conference on Applications, technologies, architectures, and protocols for computer communications
Sampling large Internet topologies for simulation purposes
Computer Networks: The International Journal of Computer and Telecommunications Networking
Measurement and analysis of online social networks
Proceedings of the 7th ACM SIGCOMM conference on Internet measurement
Network monitoring using traffic dispersion graphs (tdgs)
Proceedings of the 7th ACM SIGCOMM conference on Internet measurement
Modeling internet topology dynamics
ACM SIGCOMM Computer Communication Review
In search of the elusive ground truth: the internet's as-level connectivity structure
SIGMETRICS '08 Proceedings of the 2008 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Discarte: a disjunctive internet cartographer
Proceedings of the ACM SIGCOMM 2008 conference on Data communication
Policy relationship annotations of predefined AS-level topologies
Computer Networks: The International Journal of Computer and Telecommunications Networking
Elasticity: topological characterization of robustness in complex networks
Proceedings of the 3rd International Conference on Bio-Inspired Models of Network, Information and Computing Sytems
Liana: a decentralized load-dependent scheduler for performance-cost optimization of grid service
The Journal of Supercomputing
Graph annotations in modeling complex network topologies
ACM Transactions on Modeling and Computer Simulation (TOMACS)
NIT: A New Internet Topology Generator
EUNICE '09 Proceedings of the 15th Open European Summer School and IFIP TC6.6 Workshop on The Internet of the Future
Generating application-specific benchmark models for complex systems
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Measurement-calibrated graph models for social network experiments
Proceedings of the 19th international conference on World wide web
On the eyeshots of BGP vantage points
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Understanding topological mesoscale features in community mining
COMSNETS'10 Proceedings of the 2nd international conference on COMmunication systems and NETworks
A benchmark diagnostic model generation system
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special issue on model-based diagnostics
Eyeball ASes: from geography to connectivity
IMC '10 Proceedings of the 10th ACM SIGCOMM conference on Internet measurement
An alternate topology generator for joint study of power grids and communication networks
CRITIS'09 Proceedings of the 4th international conference on Critical information infrastructures security
Characterising the robustness of complex networks
International Journal of Internet Technology and Secured Transactions
Discriminating graphs through spectral projections
Computer Networks: The International Journal of Computer and Telecommunications Networking
SIMROT: a scalable inter-domain routing toolbox
ACM SIGMETRICS Performance Evaluation Review - Special Issue on IFIP PERFORMANCE 2011- 29th International Symposium on Computer Performance, Modeling, Measurement and Evaluation
Proceedings of the 2011 International Workshop on Modeling, Analysis, and Control of Complex Networks
Generating constrained random graphs using multiple edge switches
Journal of Experimental Algorithmics (JEA)
Sharing graphs using differentially private graph models
Proceedings of the 2011 ACM SIGCOMM conference on Internet measurement conference
Queuing network of scale free topology: on modelling large scale network
The Journal of Supercomputing
Obtaining provably legitimate internet topologies
IEEE/ACM Transactions on Networking (TON)
Review: A critical look at power law modelling of the Internet
Computer Communications
Constructing and sampling graphs with a prescribed joint degree distribution
Journal of Experimental Algorithmics (JEA)
Differentiating complex network models: An engineering perspective
Computers & Mathematics with Applications
Evolution of social-attribute networks: measurements, modeling, and implications using google+
Proceedings of the 2012 ACM conference on Internet measurement conference
Modeling Social Network Interaction Graphs
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
Analyzing the social ties and structure of contributors in open source software community
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
Analyzing Communication Interaction Networks (CINs) in enterprises and inferring hierarchies
Computer Networks: The International Journal of Computer and Telecommunications Networking
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Researchers have proposed a variety of metrics to measure important graph properties, for instance, in social, biological, and computer networks. Values for a particular graph metric may capture a graph's resilience to failure or its routing efficiency. Knowledge of appropriate metric values may influence the engineering of future topologies, repair strategies in the face of failure, and understanding of fundamental properties of existing networks. Unfortunately, there are typically no algorithms to generate graphs matching one or more proposed metrics and there is little understanding of the relationships among individual metrics or their applicability to different settings. We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d capture progressively more properties of G at the cost of more complex representation of the probability distribution. Using this series, we can quantitatively measure the distance between two graphs and construct random graphs that accurately reproduce virtually all metrics proposed in the literature. The nature of the dK-series implies that it will also capture any future metrics that may be proposed. Using our approach, we construct graphs for d=0, 1, 2, 3 and demonstrate that these graphs reproduce, with increasing accuracy, important properties of measured and modeled Internet topologies. We find that the d=2 case is sufficient for most practical purposes, while d=3 essentially reconstructs the Internet AS-and router-level topologies exactly. We hope that a systematic method to analyze and synthesize topologies offers a significant improvement to the set of tools available to network topology and protocol researchers.