# Relations Between Adjacency and Modularity Graph Partitioning

arXiv: https://arxiv.org/abs/1505.03481 · HTML: https://mlsanity.com/paper/1505.03481/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2015.

## Built on by (most cited first, 2 of 2)

- [Constant Approximation for Normalized Modularity and Associations Clustering](https://mlsanity.com/paper/2212.14334/) (2022)
- [Constructing the Truth: Text Mining and Linguistic Networks in Public Hearings of Case 03 of the Special Jurisdiction for Peace (JEP)](https://mlsanity.com/paper/2504.04325/) (2025)

## Abstract (arXiv)

This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the modularity matrix, and we derive the error of the approximation. There is also a complete proof of the equivalence between normalized adjacency clustering and normalized modularity clustering. Numerical experiments show that normalized adjacency clustering can be as twice efficient as normalized modularity clustering.