Graph Clustering with Surprise: Complexity and Exact Solutions
Data Structures and Algorithms
2013-10-23 v1
Abstract
Clustering graphs based on a comparison of the number of links within clusters and the expected value of this quantity in a random graph has gained a lot of attention and popularity in the last decade. Recently, Aldecoa and Marin proposed a related, but slightly different approach leading to the quality measure surprise, and reported good behavior in the context of synthetic and real world benchmarks. We show that the problem of finding a clustering with optimum surprise is NP-hard. Moreover, a bicriterial view on the problem permits to compute optimum solutions for small instances by solving a small number of integer linear programs, and leads to a polynomial time algorithm on trees.
Cite
@article{arxiv.1310.6019,
title = {Graph Clustering with Surprise: Complexity and Exact Solutions},
author = {Tobias Fleck and Andrea Kappes and Dorothea Wagner},
journal= {arXiv preprint arXiv:1310.6019},
year = {2013}
}