Models of similarity in complex networks

Area of Science:

• Network analysis
• Complex systems
• Graph theory

Background:

• Complex systems evolve over time, necessitating network analysis to assess sustainability.
• Existing studies compare limited network similarity measures; this work expands the scope.
• Understanding network changes is crucial for identifying stable periods.

Purpose of the Study:

• To extend existing studies by comparing a comprehensive set of 39 graph distance measures.
• To evaluate the performance of these measures on various graph types, including real-world networks.
• To identify which similarity measures are suitable for analyzing large-scale networks.

Main Methods:

• Comparison of 39 graph distance measures.
• Evaluation on simple graphs, random graph models, and real-world networks.
• Performance assessment for applicability to large networks.

Main Results:

• Many graph similarity measures, despite differing natures, show strong correlations.
• Comprehensive network similarity methods align well with simpler models.
• Key insights into the advantages and disadvantages of existing similarity models were revealed.

Conclusions:

• The study provides a better understanding of graph similarity measures for network analysis.
• Findings aid in selecting appropriate similarity measures for network structures.
• Results can inform the development of novel models for network similarity assessment.