On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Enumerating all connected maximal common subgraphs in two graphs
Theoretical Computer Science
Algorithm 457: finding all cliques of an undirected graph
Communications of the ACM
Algorithms for k-colouring and finding maximal independent sets
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Finding All Maximal Cliques in Dynamic Graphs
Computational Optimization and Applications
Evolution of Networks: From Biological Nets to the Internet and WWW (Physics)
Evolution of Networks: From Biological Nets to the Internet and WWW (Physics)
The worst-case time complexity for generating all maximal cliques and computational experiments
Theoretical Computer Science - Computing and combinatorics
Note: A note on the problem of reporting maximal cliques
Theoretical Computer Science
Large maximal cliques enumeration in sparse graphs
Proceedings of the 17th ACM conference on Information and knowledge management
A scalable, parallel algorithm for maximal clique enumeration
Journal of Parallel and Distributed Computing
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Computational Biology and Chemistry
K-isomorphism: privacy preserving network publication against structural attacks
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
Triangle listing in massive networks and its applications
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Finding maximal cliques in massive networks
ACM Transactions on Database Systems (TODS)
Relational approach for shortest path discovery over large graphs
Proceedings of the VLDB Endowment
Efficient processing of distance queries in large graphs: a vertex cover approach
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
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
Fast algorithms for maximal clique enumeration with limited memory
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
K-reach: who is in your small world
Proceedings of the VLDB Endowment
Triangle listing in massive networks
ACM Transactions on Knowledge Discovery from Data (TKDD) - Special Issue on the Best of SIGKDD 2011
Efficient breadth-first search on large graphs with skewed degree distributions
Proceedings of the 16th International Conference on Extending Database Technology
Online search of overlapping communities
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
TF-Label: a topological-folding labeling scheme for reachability querying in a large graph
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
Efficiently computing k-edge connected components via graph decomposition
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
Redundancy-aware maximal cliques
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Graph-based informative-sentence selection for opinion summarization
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
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Maximal clique enumeration (MCE) is a fundamental problem in graph theory and has important applications in many areas such as social network analysis and bioinformatics. The problem is extensively studied; however, the best existing algorithms require memory space linear in the size of the input graph. This has become a serious concern in view of the massive volume of today's fast-growing network graphs. Since MCE requires random access to different parts of a large graph, it is difficult to divide the graph into smaller parts and process one part at a time, because either the result may be incorrect and incomplete, or it incurs huge cost on merging the results from different parts. We propose a novel notion, H*-graph, which defines the core of a network and extends to encompass the neighborhood of the core for MCE computation. We propose the first external-memory algorithm for MCE (ExtMCE) that uses the H*-graph to bound the memory usage. We prove both the correctness and completeness of the result computed by ExtMCE. Extensive experiments verify that ExtMCE efficiently processes large networks that cannot be fit in the memory. We also show that the H*-graph captures important properties of the network; thus, updating the maximal cliques in the H*-graph retains the most essential information, with a low update cost, when it is infeasible to perform update on the entire network.