Multi-Relational Structural Entropy

TL;DR

This paper introduces Multi-relational Structural Entropy (MrSE), a novel metric that captures the heterogeneity of relations in multi-relational graphs, improving structural understanding and task performance.

Contribution

It extends Structural Entropy to multi-relational graphs by incorporating relation types, providing a new interpretative metric and a greedy optimization algorithm.

Findings

MrSE offers more insightful graph structure interpretation.

Enhances node clustering and social event detection performance.

Outperforms traditional SE in multi-relational contexts.

Abstract

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.