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
Efficiently Mining Maximal Frequent Itemsets
ICDM '01 Proceedings of the 2001 IEEE International Conference on Data Mining
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
Segmentation and Automated Social Hierarchy Detection through Email Network Analysis
Advances in Web Mining and Web Usage Analysis
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
An efficient branch-and-bound algorithm for finding a maximum clique
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Finding maximal cliques in massive networks by H*-graph
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
A new algorithm for enumerating all maximal cliques in complex network
ADMA'06 Proceedings of the Second international conference on Advanced Data Mining and Applications
Computational Biology and Chemistry
Triangle listing in massive networks and its applications
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
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
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
Redundancy-aware maximal cliques
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
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Maximal clique enumeration 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 networks. We propose a general framework for designing external-memory algorithms for maximal clique enumeration in large graphs. The general framework enables maximal clique enumeration to be processed recursively in small subgraphs of the input graph, thus allowing in-memory computation of maximal cliques without the costly random disk access. We prove that the set of cliques obtained by the recursive local computation is both correct (i.e., globally maximal) and complete. The subgraph to be processed each time is defined based on a set of base vertices that can be flexibly chosen to achieve different purposes. We discuss the selection of the base vertices to fully utilize the available memory in order to minimize I/O cost in static graphs, and for update maintenance in dynamic graphs. We also apply our framework to design an external-memory algorithm for maximum clique computation in a large graph.