# Multi-Relational Structural Entropy

arXiv: https://arxiv.org/abs/2405.07096 · HTML: https://mlsanity.com/paper/2405.07096/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2024.

## Built on by (most cited first, 3 of 3)

- [Effective Exploration Based on the Structural Information Principles](https://mlsanity.com/paper/2410.06621/) (2024)
- [The End of Reward Engineering: How LLMs Are Redefining Multi-Agent Coordination](https://mlsanity.com/paper/2601.08237/) (2026)
- [When LLM Meets Tree Search: A Systematic View of Inference as Search in Large Language Models](https://mlsanity.com/paper/2608.30395/) (2026)

## Abstract (arXiv)

Structural Entropy (SE) measures the structural information contained in a graph. Minimizing or maximizing SE helps to reveal or obscure the intrinsic structural patterns underlying graphs in an interpretable manner, finding applications in various tasks driven by networked data. However, SE ignores the heterogeneity inherent in the graph relations, which is ubiquitous in modern networks. In this work, we extend SE to consider heterogeneous relations and propose the first metric for multi-relational graph structural information, namely, Multi-relational Structural Entropy (MrSE). To this end, we first cast SE through the novel lens of the stationary distribution from random surfing, which readily extends to multi-relational networks by considering the choices of both nodes and relation types simultaneously at each step. The resulting MrSE is then optimized by a new greedy algorithm to reveal the essential structures within a multi-relational network. Experimental results highlight that the proposed MrSE offers a more insightful interpretation of the structure of multi-relational graphs compared to SE. Additionally, it enhances the performance of two tasks that involve real-world multi-relational graphs, including node clustering and social event detection.