On the expected behavior of disjoint set union algorithms
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Size and connectivity of the k-core of a random graph
Discrete Mathematics
Journal of the ACM (JACM)
Global min-cuts in RNC, and other ramifications of a simple min-out algorithm
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Experimental study of minimum cut algorithms
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On the average behavior of set merging algorithms (Extended Abstract)
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
The webgraph framework I: compression techniques
Proceedings of the 13th international conference on World Wide Web
Group formation in large social networks: membership, growth, and evolution
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Graph evolution: Densification and shrinking diameters
ACM Transactions on Knowledge Discovery from Data (TKDD)
Extraction and classification of dense communities in the web
Proceedings of the 16th international conference on World Wide Web
On triangulation-based dense neighborhood graph discovery
Proceedings of the VLDB Endowment
Proceedings of the 20th international conference on World wide web
Efficient core decomposition in massive networks
ICDE '11 Proceedings of the 2011 IEEE 27th International Conference on Data Engineering
An advanced network visualization system for financial crime detection
PACIFICVIS '11 Proceedings of the 2011 IEEE Pacific Visualization Symposium
Finding maximal k-edge-connected subgraphs from a large graph
Proceedings of the 15th International Conference on Extending Database Technology
Truss decomposition in massive networks
Proceedings of the VLDB Endowment
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Capturing sets of closely related vertices from large networks is an essential task in many applications such as social network analysis, bioinformatics, and web link research. Decomposing a graph into k-core components is a standard and efficient method for this task, but obtained clusters might not be well-connected. The idea of using maximal k-edge-connected subgraphs was recently proposed to address this issue. Although we can obtain better clusters with this idea, the state-of-the-art method is not efficient enough to process large networks with millions of vertices. In this paper, we propose a new method to decompose a graph into maximal k-edge-connected components, based on random contraction of edges. Our method is simple to implement but improves performance drastically. We experimentally show that our method can successfully decompose large networks and it is thousands times faster than the previous method. Also, we theoretically explain why our method is efficient in practice. To see the importance of maximal k-edge-connected subgraphs, we also conduct experiments using real-world networks to show that many k-core components have small edge-connectivity and they can be decomposed into a lot of maximal k-edge-connected subgraphs.