On power-law relationships of the Internet topology
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The ubiquitous Kronecker product
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
The "DGX" distribution for mining massive, skewed data
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Extracting Large-Scale Knowledge Bases from the Web
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
ANF: a fast and scalable tool for data mining in massive graphs
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The Kronecker product and stochastic automata networks
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Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
The web as a graph: measurements, models, and methods
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Graph mining: Laws, generators, and algorithms
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Graph evolution: Densification and shrinking diameters
ACM Transactions on Knowledge Discovery from Data (TKDD)
Scalable modeling of real graphs using Kronecker multiplication
Proceedings of the 24th international conference on Machine learning
Densification arising from sampling fixed graphs
SIGMETRICS '08 Proceedings of the 2008 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Weighted graphs and disconnected components: patterns and a generator
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Description and simulation of dynamic mobility networks
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On the Synthetic Generation of Semantic Web Schemas
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A methodology to identify characteristics of the dynamic of mobile networks
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A Dynamic Model for On-Line Social Networks
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ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
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RTG: a recursive realistic graph generator using random typing
Data Mining and Knowledge Discovery
RTG: A Recursive Realistic Graph Generator Using Random Typing
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part I
Games on graphs that grow deterministically
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
A Survey of Statistical Network Models
Foundations and Trends® in Machine Learning
Kronecker Graphs: An Approach to Modeling Networks
The Journal of Machine Learning Research
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Deterministic decentralized search in random graphs
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Generalizing Kronecker graphs in order to model searchable networks
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
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A geometric model for on-line social networks
WOSN'10 Proceedings of the 3rd conference on Online social networks
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ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part I
HADI: Mining Radii of Large Graphs
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Milgram-routing in social networks
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WAW'11 Proceedings of the 8th international conference on Algorithms and models for the web graph
Spectral analysis for billion-scale graphs: discoveries and implementation
PAKDD'11 Proceedings of the 15th Pacific-Asia conference on Advances in knowledge discovery and data mining - Volume Part II
Unifying guilt-by-association approaches: theorems and fast algorithms
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The university of Florida sparse matrix collection
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NOVA: a novel and efficient framework for finding subgraph isomorphism mappings in large graphs
DASFAA'10 Proceedings of the 15th international conference on Database Systems for Advanced Applications - Volume Part I
Scale invariant bipartite graph generative model
SIIS'11 Proceedings of the 2011 international conference on Security and Intelligent Information Systems
Giant components in Kronecker graphs
Random Structures & Algorithms
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Reachability analysis and modeling of dynamic event networks
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Inexact subgraph isomorphism in MapReduce
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An in-depth analysis of stochastic Kronecker graphs
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ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
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Information diffusion on the iterated local transitivity model of online social networks
Discrete Applied Mathematics
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Network topology models for multihop wireless networks
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Learning mixed kronecker product graph models with simulated method of moments
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Direction-optimizing breadth-first search
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How can we generate realistic graphs? In addition, how can we do so with a mathematically tractable model that makes it feasible to analyze their properties rigorously? Real graphs obey a long list of surprising properties: Heavy tails for the in- and out-degree distribution; heavy tails for the eigenvalues and eigenvectors; small diameters; and the recently discovered “Densification Power Law” (DPL). All published graph generators either fail to match several of the above properties, are very complicated to analyze mathematically, or both. Here we propose a graph generator that is mathematically tractable and matches this collection of properties. The main idea is to use a non-standard matrix operation, the Kronecker product, to generate graphs that we refer to as “Kronecker graphs”. We show that Kronecker graphs naturally obey all the above properties; in fact, we can rigorously prove that they do so. We also provide empirical evidence showing that they can mimic very well several real graphs.