A Path-Based Distribution Measure for Network Comparison.

Area of Science:

• Network Science
• Computational Social Science
• Data Analysis

Background:

• Analyzing multiple networks is increasingly common due to rising data volumes.
• Existing network comparison methods quantify structural topological differences.
• Quantifying network dissimilarity is crucial for understanding complex systems.

Purpose of the Study:

• To propose novel network comparison measures based on shortest path distributions and node centrality.
• To quantify global topological differences using local network features.
• To define network distance and network entropy for characterizing network systems.

Main Methods:

• Utilizing shortest path distributions combined with node centrality measures.
• Defining network distance to quantify dissimilarities between networks.
• Defining network entropy to characterize typical network system states.

Main Results:

• The proposed network distance effectively discriminates networks generated by different models.
• Incorporating end-node information along paths enhances network dissimilarity detection.
• Network entropy successfully identifies tipping points in synthetic network evolution.
• The measures are effective for multilayer network reduction and temporal network state identification.

Conclusions:

• The novel network comparison measures capture both global and local network topological features.
• These methods provide effective tools for quantifying network dissimilarity and characterizing network dynamics.
• The approach demonstrates utility in network reduction and identifying system states in complex networks.