# A Method Based on Total Variation for Network Modularity Optimization using the MBO Scheme

arXiv: https://arxiv.org/abs/1304.4679 · HTML: https://mlsanity.com/paper/1304.4679/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2013.

## Built on by (most cited first, 4 of 4)

- [On the existence of solutions to adversarial training in multiclass classification](https://mlsanity.com/paper/2305.00075/) (2023)
- [Rates of Convergence for Regression with the Graph Poly-Laplacian](https://mlsanity.com/paper/2209.02305/) (2022)
- [Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian](https://mlsanity.com/paper/2401.07463/) (2024)
- [MALADY: Multiclass Active Learning with Auction Dynamics on Graphs](https://mlsanity.com/paper/2409.09475/) (2024)

## Abstract (arXiv)

The study of network structure is pervasive in sociology, biology, computer science, and many other disciplines. One of the most important areas of network science is the algorithmic detection of cohesive groups of nodes called "communities". One popular approach to find communities is to maximize a quality function known as em modularity to achieve some sort of optimal clustering of nodes. In this paper, we interpret the modularity function from a novel perspective: we reformulate modularity optimization as a minimization problem of an energy functional that consists of a total variation term and an ℓ2 balance term. By employing numerical techniques from image processing and ℓ1 compressive sensing -- such as convex splitting and the Merriman-Bence-Osher (MBO) scheme -- we develop a variational algorithm for the minimization problem. We present our computational results using both synthetic benchmark networks and real data.