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On the min-entropy of equilibrium graphs in network creation games
Chuang-Chieh Lin1, Chih-Chieh Hung2,3
1Department of Computer Science and Engineering, National Taiwan Ocean University, No. 2, Beining Rd., Jhongjheng Dist., Keelung City, 202301, Taiwan.
Scientific Reports
|March 22, 2026
Summary
This study introduces Equilibrium Graph Min-Entropy (EGME) to measure network complexity in strategic network formation. EGME effectively quantifies structural variations and network stability across different cost parameters.
Area of Science:
- Network Science
- Game Theory
- Information Theory
Background:
- Classical network creation models analyze strategic agent behavior.
- Quantifying structural complexity in emergent networks remains a challenge.
Purpose of the Study:
- To introduce and analyze Equilibrium Graph Min-Entropy (EGME) as a novel metric for network structural complexity.
- To investigate EGME's behavior across different network formation game parameters.
Main Methods:
- Defining EGME based on social cost distributions in equilibrium graphs.
- Deriving exact characterizations and bounds for EGME under various edge-cost regimes.
- Conducting simulation experiments to validate EGME's correlation with network properties.
Main Results:
- EGME provides exact characterizations for small edge costs and general bounds for larger costs.
- Simulations show EGME distinguishes structural variations due to network size and edge costs.
- EGME correlates strongly with graph density, diameter, and betweenness centrality.
Conclusions:
- EGME is a robust measure for assessing structural complexity in strategic network formation.
- EGME offers insights into network stability and structural properties.
- The metric is effective in distinguishing network variations induced by parameter changes.
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