Sparsest cuts and bottlenecks in graphs
Discrete Applied Mathematics - Computational combinatiorics
Algorithms for graph partitioning on the planted partition model
Random Structures & Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An Efficient Practical Heuristic For Good Ratio-Cut Partitioning
VLSID '03 Proceedings of the 16th International Conference on VLSI Design
Empirical Evaluation of Graph Partitioning Using Spectral Embeddings and Flow
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
On defining and computing communities
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
| Hi-index | 0.00 |
We say that there is a community structure in a graph when the nodes of the graph can be partitioned into groups (communities) such that each group is internally more densely connected than with the rest of the graph. However, the challenge is to specify what is to be dense, and what is relatively more connected (there seems to exist an analogous situation to what is a cluster in unsupervized learning). Recently, Olsen (2012) provided a general definition that seemed to be significantly more generic that others. We make two observations regarding such definition. (1) First, we show that finding a community structure with two equal size communities is NP-complete (Uniform 2-Communities). The first implication of this is that finding a large community seems intractable. The second implication is that, since this is a hardness result for k = 2, the Uniform k-Communities problem is not fixed-parameter tractable when k is the parameter. (2) The second observation is that communities are not required to be connected in Olsen (2012)'s definition. However, we indicate that our result holds as well as the results by Olsen (2012) when we require communities to be connected, and we show examples where using connected communities seems more natural.