# Modularity Optimization as a Training Criterion for Graph Neural Networks

arXiv: https://arxiv.org/abs/2207.00107 · HTML: https://mlsanity.com/paper/2207.00107/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 30 Jun 2022.

## Builds on (most cited first, 6 of 6)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [A Unified Framework for Community Detection and Network Representation Learning](https://mlsanity.com/paper/1611.06645/) (2016)

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

- [The Map Equation Goes Neural: Mapping Network Flows with Graph Neural Networks](https://mlsanity.com/paper/2310.01144/) (2023)
- [ModTGCN: Modularity-aware Graph Neural Networks for Text Classification](https://mlsanity.com/paper/2606.23694/) (2026)

## Abstract (arXiv)

Graph convolution is a recent scalable method for performing deep feature learning on attributed graphs by aggregating local node information over multiple layers. Such layers only consider attribute information of node neighbors in the forward model and do not incorporate knowledge of global network structure in the learning task. In particular, the modularity function provides a convenient source of information about the community structure of networks. In this work we investigate the effect on the quality of learned representations by the incorporation of community structure preservation objectives of networks in the graph convolutional model. We incorporate the objectives in two ways, through an explicit regularization term in the cost function in the output layer and as an additional loss term computed via an auxiliary layer. We report the effect of community structure preserving terms in the graph convolutional architectures. Experimental evaluation on two attributed bibilographic networks showed that the incorporation of the community-preserving objective improves semi-supervised node classification accuracy in the sparse label regime.