Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
DOULION: counting triangles in massive graphs with a coin
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
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
Kronecker Graphs: An Approach to Modeling Networks
The Journal of Machine Learning Research
Proceedings of the 19th international conference on World wide web
Efficient algorithms for large-scale local triangle counting
ACM Transactions on Knowledge Discovery from Data (TKDD)
Clustering coefficient queries on massive dynamic social networks
WAIM'10 Proceedings of the 11th international conference on Web-age information management
HADI: Mining Radii of Large Graphs
ACM Transactions on Knowledge Discovery from Data (TKDD)
Journal of the ACM (JACM)
Expansion properties of large social graphs
DASFAA'11 Proceedings of the 16th international conference on Database systems for advanced applications
Structural trend analysis for online social networks
Proceedings of the VLDB Endowment
A spectral algorithm for computing social balance
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
Colorful triangle counting and a MapReduce implementation
Information Processing Letters
Managing and mining large graphs: patterns and algorithms
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
Degree relations of triangles in real-world networks and graph models
Proceedings of the 21st ACM international conference on Information and knowledge management
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
On the streaming complexity of computing local clustering coefficients
Proceedings of the sixth ACM international conference on Web search and data mining
Presto: distributed machine learning and graph processing with sparse matrices
Proceedings of the 8th ACM European Conference on Computer Systems
Big graph mining: algorithms and discoveries
ACM SIGKDD Explorations Newsletter
A space efficient streaming algorithm for triangle counting using the birthday paradox
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Using social network knowledge for detecting spider constructions in social security fraud
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
Realtime analysis of information diffusion in social media
Proceedings of the VLDB Endowment
Why do simple algorithms for triangle enumeration work in the real world?
Proceedings of the 5th conference on Innovations in theoretical computer science
Skew strikes back: new developments in the theory of join algorithms
ACM SIGMOD Record
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Triangles are important for real world social networks, lying at the heart of the clustering coefficient and of the transitivity ratio. However, straight-forward and even approximate counting algorithms can be slow, trying to execute or approximate the equivalent of a 3-way database join. In this paper, we provide two algorithms, the Eigen Triangle for counting the total number of triangles in a graph, and the Eigen Triangle Local algorithm that gives the count of triangles that contain a desired node. Additional contributions include the following:(a) We show that both algorithms achieve excellent accuracy, with up to ~1000x faster execution time, on several, real graphs and (b) we discover two new power laws (Degree-Triangle and Triangle Participation laws) with surprising properties.