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Normalized Sombor Indices as Complexity Measures of Random Networks
R Aguilar-Sánchez1, J A Méndez-Bermúdez2, José M Rodríguez3
1Facultad de Ciencias Químicas, Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico.
Entropy (Basel, Switzerland)
|August 27, 2021
Summary
This study explores Sombor indices on random networks, finding normalized values correlate with network complexity and Shannon entropy. These Sombor indices offer insights into network structure and information content.
Area of Science:
- Network science
- Graph theory
- Computational mathematics
Background:
- Sombor indices are novel graph invariants.
- Random networks are fundamental models in network science.
- Understanding network complexity is crucial for various applications.
Purpose of the Study:
- To computationally investigate Sombor indices on three distinct random network models.
- To analyze the scaling behavior of normalized Sombor indices with network properties.
- To evaluate Sombor indices as potential measures of network complexity.
Main Methods:
- Application of Sombor indices to Erdös-Rényi networks, random geometric graphs, and bipartite random networks.
- Utilizing statistical random matrix theory for analysis.
- Correlating Sombor indices with Shannon entropy of adjacency matrix eigenvectors.
Main Results:
- Normalized average Sombor indices scale with the average degree of the random networks.
- Selected normalized Sombor indices demonstrate a strong correlation with Shannon entropy.
- The study establishes a link between Sombor indices and network complexity.
Conclusions:
- Sombor indices provide valuable insights into the structural properties of random networks.
- Normalized Sombor indices can serve as effective complexity measures for these networks.
- The findings suggest potential applications in information theory and network analysis.
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