Data mining: concepts and techniques
Data mining: concepts and techniques
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Genetic, Iterated and Multistart Local Search for the Maximum Clique Problem
Proceedings of the Applications of Evolutionary Computing on EvoWorkshops 2002: EvoCOP, EvoIASP, EvoSTIM/EvoPLAN
Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
An Improved Ant Colony Optimization for the Maximum Clique Problem
ICNC '07 Proceedings of the Third International Conference on Natural Computation - Volume 04
An effective local search for the maximum clique problem
Information Processing Letters
An algorithm for finding a maximum clique in a graph
Operations Research Letters
Survey of clustering algorithms
IEEE Transactions on Neural Networks
A Biologically Inspired Measure for Coexpression Analysis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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An important problem of knowledge discovery that has recently evolved in various reallife networks is identifying the largest set of vertices that are functionally associated. The topology of many real-life networks shows scale-freeness, where the vertices of the underlying graph follow a power-law degree distribution. Moreover, the graphs corresponding to most of the real-life networks are weighted in nature. In this article, the problem of finding the largest group or association of vertices that are dense (denoted as dense vertexlet) in a weighted scale-free graph is addressed. Density quantifies the degree of similarity within a group of vertices in a graph. The density of a vertexlet is defined in a novel way that ensures significant participation of all the vertices within the vertexlet. It is established that the problem is NP-complete in nature. An upper bound on the order of the largest dense vertexlet of a weighted graph, with respect to certain density threshold value, is also derived. Finally, an O(n$^2$ log n) (n denotes the number of vertices in the graph) heuristic graph mining algorithm that produces an approximate solution for the problem is presented.