Detectability of the spectral method for sparse graph partitioning
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology 4259-G5-22, Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8502, Japan
Received: 22 September 2015
Accepted: 16 November 2015
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.
PACS: 02.70.Hm – Spectral methods / 89.75.Hc – Networks and genealogical trees / 89.20.-a – Interdisciplinary applications of physics
© EPLA, 2015