Self-similarity in World Wide Web traffic: evidence and possible causes
IEEE/ACM Transactions on Networking (TON)
Some remarks on the Kronecker product of graphs
Information Processing Letters
Factoring cardinal product graphs in polynomial time
Proceedings of the conference on Discrete metric spaces
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Proceedings of the 9th international World Wide Web conference on Computer networks : the international journal of computer and telecommunications netowrking
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
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
ACM Transactions on Internet Technology (TOIT)
IEEE Internet Computing
Extracting Large-Scale Knowledge Bases from the Web
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
ANF: a fast and scalable tool for data mining in massive graphs
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
Stochastic models for the Web graph
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
The Small-World Phenomenon: An Algorithmic Perspective
The Small-World Phenomenon: An Algorithmic Perspective
ACM SIGKDD Explorations Newsletter
The Kronecker product and stochastic automata networks
Journal of Computational and Applied Mathematics
Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Graph model selection using maximum likelihood
ICML '06 Proceedings of the 23rd international conference on Machine learning
Group formation in large social networks: membership, growth, and evolution
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Structure and evolution of online social networks
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
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
Statistical properties of community structure in large social and information networks
Proceedings of the 17th international conference on World Wide Web
Fast Counting of Triangles in Large Real Networks without Counting: Algorithms and Laws
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Proof of a conjecture concerning the direct product of bipartite graphs
European Journal of Combinatorics
Co-evolution of social and affiliation networks
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Networks, communities and kronecker products
Proceedings of the 1st ACM international workshop on Complex networks meet information & knowledge management
The web as a graph: measurements, models, and methods
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
A geometric preferential attachment model of networks II
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Random dot product graph models for social networks
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Realistic, mathematically tractable graph generation and evolution, using kronecker multiplication
PKDD'05 Proceedings of the 9th European conference on Principles and Practice of Knowledge Discovery in Databases
A Survey of Statistical Network Models
Foundations and Trends® in Machine Learning
Brief paper: Design of highly synchronizable and robust networks
Automatica (Journal of IFAC)
A discussion on the design of graph database benchmarks
TPCTC'10 Proceedings of the Second TPC technology conference on Performance evaluation, measurement and characterization of complex systems
Symmetrizations for clustering directed graphs
Proceedings of the 14th International Conference on Extending Database Technology
On the privacy of anonymized networks
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Automatic text summarization and small-world networks
Proceedings of the 11th ACM symposium on Document engineering
On the super connectivity of Kronecker products of graphs
Information Processing Letters
Structural properties of the scale-free Barabasi-Albert graph
Automation and Remote Control
Towards trust inference from bipartite social networks
DBSocial '12 Proceedings of the 2nd ACM SIGMOD Workshop on Databases and Social Networks
Constructing and sampling graphs with a prescribed joint degree distribution
Journal of Experimental Algorithmics (JEA)
The missing models: a data-driven approach for learning how networks grow
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Streaming graph partitioning for large distributed graphs
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Realizing Large-Scale Interactive Network Simulation via Model Splitting
PADS '12 Proceedings of the 2012 ACM/IEEE/SCS 26th Workshop on Principles of Advanced and Distributed Simulation
Breaking the speed and scalability barriers for graph exploration on distributed-memory machines
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Evolution of social-attribute networks: measurements, modeling, and implications using google+
Proceedings of the 2012 ACM conference on Internet measurement conference
Human activities as stochastic kronecker graphs
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Network analysis on provenance graphs from a crowdsourcing application
IPAW'12 Proceedings of the 4th international conference on Provenance and Annotation of Data and Processes
Inexact subgraph isomorphism in MapReduce
Journal of Parallel and Distributed Computing
On modeling product advertisement in large-scale online social networks
IEEE/ACM Transactions on Networking (TON)
Structure and dynamics of information pathways in online media
Proceedings of the sixth ACM international conference on Web search and data mining
Transforming graph data for statistical relational learning
Journal of Artificial Intelligence Research
An in-depth analysis of stochastic Kronecker graphs
Journal of the ACM (JACM)
Naturality of Network Creation Games, Measurement and Analysis
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
Mizan: a system for dynamic load balancing in large-scale graph processing
Proceedings of the 8th ACM European Conference on Computer Systems
GraphBuilder: scalable graph ETL framework
First International Workshop on Graph Data Management Experiences and Systems
Performance introspection of graph databases
Proceedings of the 6th International Systems and Storage Conference
Learning mixed kronecker product graph models with simulated method of moments
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Towards highly scalable pregel-based graph processing platform with x10
Proceedings of the 22nd international conference on World Wide Web companion
Community detection in content-sharing social networks
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
Efficient breadth first search on multi-GPU systems
Journal of Parallel and Distributed Computing
On the precision of social and information networks
Proceedings of the first ACM conference on Online social networks
A dependability evaluation tool for the Internet of Things
Computers and Electrical Engineering
Decompositions of triangle-dense graphs
Proceedings of the 5th conference on Innovations in theoretical computer science
On computing the diameter of real-world undirected graphs
Theoretical Computer Science
Attributed graph models: modeling network structure with correlated attributes
Proceedings of the 23rd international conference on World wide web
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How can we generate realistic networks? In addition, how can we do so with a mathematically tractable model that allows for rigorous analysis of network properties? Real networks exhibit 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 densification and shrinking diameters over time. Current network models and generators either fail to match several of the above properties, are complicated to analyze mathematically, or both. Here we propose a generative model for networks that is both mathematically tractable and can generate networks that have all the above mentioned structural properties. Our main idea here is to use a non-standard matrix operation, the Kronecker product, to generate graphs which we refer to as "Kronecker graphs". First, we show that Kronecker graphs naturally obey common network properties. In fact, we rigorously prove that they do so. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KRONFIT, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super-exponential time. In contrast, KRONFIT takes linear time, by exploiting the structure of Kronecker matrix multiplication and by using statistical simulation techniques. Experiments on a wide range of large real and synthetic networks show that KRONFIT finds accurate parameters that very well mimic the properties of target networks. In fact, using just four parameters we can accurately model several aspects of global network structure. Once fitted, the model parameters can be used to gain insights about the network structure, and the resulting synthetic graphs can be used for null-models, anonymization, extrapolations, and graph summarization.