Fractional information dimensions of complex networks
Aldo Ramirez-Arellano1, José María Sigarreta Almira2, Juan Bory-Reyes3
1SEPI-UPIICSA, Instituto Politécnico Nacional, Ciudad de México C.P. 08400, Mexico.
Chaos (Woodbury, N.Y.)
|October 2, 2020
Summary
This study introduces fractional information dimensions for complex networks, offering a novel way to analyze network structures. These new dimensions provide deeper insights compared to traditional methods using Shannon entropy.
Area of Science:
- Complex networks analysis
- Information theory
- Fractional calculus
Background:
- Complex networks are ubiquitous in nature and technology.
- Understanding their structure is crucial for various applications.
- Existing methods like Shannon entropy-based information dimension have limitations.
Purpose of the Study:
- To introduce novel information dimensions for complex networks.
- To utilize fractional order entropies for network analysis.
- To compare the efficacy of fractional information dimensions against classic methods.
Main Methods:
- Application of fractional order entropies to define new information dimensions.
- Analysis of real and synthetic complex networks.
- Comparison with Shannon entropy-based information dimension.
Main Results:
- Fractional information dimensions reveal new structural properties of complex networks.
- The proposed method offers a more nuanced analysis compared to traditional approaches.
- A classification of complex networks based on fractional information dimensions was established.
Conclusions:
- Fractional information dimensions provide a powerful new tool for complex network analysis.
- This approach enhances our understanding of network complexity.
- The findings facilitate a more detailed classification of network structures.
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