During discussion among reviewers, two concerns are focused and discussed: (1) the proposed formulation is limited to the case of k = 2; (2) experiments are not thorough. The limitation of (1) is a standard assumption for SBM models and it can be acceptable. In addition, the concern (2) is also acceptable as evaluating Louvain itself is not the scope of the paper, and the main contribution of this paper is theoretical analysis of Louvain. Hence I recommend acceptance of the paper. All reviewers agree that presentation can be improved. So I strongly recommend to revise the paper by referring reviews.