# Differentiable Tripartite Modularity for Clustering Heterogeneous Graphs

arXiv: https://arxiv.org/abs/2602.09864 · HTML: https://mlsanity.com/paper/2602.09864/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 12 references that are in the map.
- First posted on arXiv 10 Feb 2026.

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

- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Graph Clustering with Graph Neural Networks](https://mlsanity.com/paper/2006.16904/) (2020)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Community detection in networks: A user guide](https://mlsanity.com/paper/1608.00163/) (2016)
- [Modularity based community detection in heterogeneous networks](https://mlsanity.com/paper/1803.07961/) (2018)

## Abstract (arXiv)

Clustering heterogeneous relational data remains a central challenge in graph learning, particularly when interactions involve more than two types of entities. While differentiable modularity objectives such as DMoN have enabled end-to-end community detection on homogeneous and bipartite graphs, extending these approaches to higher-order relational structures remains non-trivial. In this work, we introduce a differentiable formulation of tripartite modularity for graphs composed of three node types connected through mediated interactions. Community structure is defined in terms of weighted co-paths across the tripartite graph, together with an exact factorized computation that avoids the explicit construction of dense third-order tensors. A structural normalization at pivot nodes is introduced to control extreme degree heterogeneity and ensure stable optimization. The resulting objective can be optimized jointly with a graph neural network in an end-to-end manner, while retaining linear complexity in the number of edges. We validate the proposed framework on large-scale urban cadastral data, where it exhibits robust convergence behavior and produces spatially coherent partitions. These results highlight differentiable tripartite modularity as a generic methodological building block for unsupervised clustering of heterogeneous graphs.