Evaluating Knowledge Graph Complexity via Semantic, Spectral, and Structural Metrics for Link Prediction

2025-08-21

AI Summary

Existing complexity measures for knowledge graph (KG) link prediction lack stability, interpretability, and strong correlation with downstream performance—particularly spectral metrics like Cumulative Spectral Gradient (CSG), which exhibit high hyperparameter sensitivity and weak correlation with MRR/Hit@1. Method: We propose novel semantic-structural complexity indicators—including relation entropy, maximum relational diversity per node, and type cardinality—and integrate them within a unified analytical framework combining Transformer-based semantic embeddings and spectral clustering. Results: Empirical evaluation shows that relation entropy and related metrics exhibit significant negative correlations with MRR and Hit@1, outperforming CSG in predictive stability and consistency; conversely, graph connectivity measures correlate positively with Hit@10. Our approach establishes a more reliable, task-aligned paradigm for KG complexity modeling, enabling principled assessment of structural and semantic intricacy in relation to link prediction efficacy.

Technology Category

• Data Mining & Knowledge Management: Linked Open Data, Knowledge Graphs & KB Completion
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Graph-based Machine Learning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Understanding dataset complexity is fundamental to evaluating and comparing link prediction models on knowledge graphs (KGs). While the Cumulative Spectral Gradient (CSG) metric, derived from probabilistic divergence between classes within a spectral clustering framework, has been proposed as a classifier agnostic complexity metric purportedly scaling with class cardinality and correlating with downstream performance, it has not been evaluated in KG settings so far. In this work, we critically examine CSG in the context of multi relational link prediction, incorporating semantic representations via transformer derived embeddings. Contrary to prior claims, we find that CSG is highly sensitive to parametrisation and does not robustly scale with the number of classes. Moreover, it exhibits weak or inconsistent correlation with standard performance metrics such as Mean Reciprocal Rank (MRR) and Hit@1. To deepen the analysis, we introduce and benchmark a set of structural and semantic KG complexity metrics. Our findings reveal that global and local relational ambiguity captured via Relation Entropy, node level Maximum Relation Diversity, and Relation Type Cardinality exhibit strong inverse correlations with MRR and Hit@1, suggesting these as more faithful indicators of task difficulty. Conversely, graph connectivity measures such as Average Degree, Degree Entropy, PageRank, and Eigenvector Centrality correlate positively with Hit@10. Our results demonstrate that CSGs purported stability and generalization predictive power fail to hold in link prediction settings and underscore the need for more stable, interpretable, and task-aligned measures of dataset complexity in knowledge driven learning.

Problem

• Evaluating knowledge graph complexity metrics for link prediction
• Assessing CSG metric sensitivity and correlation with performance
• Introducing structural and semantic metrics as better complexity indicators

Innovation

• Evaluated spectral clustering complexity metric CSG
• Introduced semantic and structural KG complexity metrics
• Benchmarked metrics against performance indicators like MRR