Detectability of the spectral method for sparse graph partitioning
Social and Information Networks
2015-12-21 v3 Statistical Mechanics
Physics and Society
Abstract
We show that modularity maximization with the resolution parameter offers a unifying framework of graph partitioning. In this framework, we demonstrate that the spectral method exhibits universal detectability, irrespective of the value of the resolution parameter, as long as the graph is partitioned. Furthermore, we show that when the resolution parameter is sufficiently small, a first-order phase transition occurs, resulting in the graph being unpartitioned.
Keywords
Cite
@article{arxiv.1509.06484,
title = {Detectability of the spectral method for sparse graph partitioning},
author = {Tatsuro Kawamoto and Yoshiyuki Kabashima},
journal= {arXiv preprint arXiv:1509.06484},
year = {2015}
}
Comments
6 pages, 2 figures