Computational Statistics & Data Analysis
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An Implementation of Logical Analysis of Data
IEEE Transactions on Knowledge and Data Engineering
Greedy approximation algorithms for finding dense components in a graph
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
SIAM Journal on Discrete Mathematics
Finding a Maximum Density Subgraph
Finding a Maximum Density Subgraph
Weighted Graph Cuts without Eigenvectors A Multilevel Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
NP-hardness of Euclidean sum-of-squares clustering
Machine Learning
On the NP-Completeness of some graph cluster measures
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Computer Science Review
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In a graph G=(V,E), the density is the ratio between the number of edges |E| and the number of vertices |V|. This criterion may be used to find communities in a graph: groups of highly connected vertices. We propose an optimization problem based on this criterion; the idea is to find the vertex partition that maximizes the sum of the densities of each class. We prove that this problem is NP-hard by giving a reduction from graph-k-colorability. Additionally, we give a polynomial time algorithm for the special case of trees.