A systematic approach to classifying and evaluating heterogeneity measures

Area of Science:

• Network Science
• Data Analysis
• Complex Systems

Background:

• Network heterogeneity analysis employs various measures.
• Existing methods may yield inconsistent results.
• A systematic approach is needed to understand these differences.

Purpose of the Study:

• Introduce a systematic framework for analyzing network heterogeneity.
• Classify heterogeneity measures into distinct groups.
• Clarify inconsistencies in measure results.

Main Methods:

• Categorized heterogeneity measures into three classes: dispersion-based, expected-difference, and divergent.
• Analyzed structural aspects captured by each measure class.
• Distinguished between degree-focused and topology-aware quantification.

Main Results:

• Demonstrated that different measure classes capture distinct structural aspects of heterogeneity.
• Graph heterogeneity measures incorporate global topology, unlike degree-focused measures.
• Apparent inconsistencies in measures stem from heterogeneity's complexity, not flaws.

Conclusions:

• The proposed framework aids in selecting context-appropriate heterogeneity measures.
• Highlights the importance of distinguishing between degree-focused and topology-aware quantification.
• Suggests developing hybrid measures for complex systems analysis.