Iterative Generation and Generalized Degree Distribution of Higher-Order Fractal Scale-Free Networks
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911634180538368 |
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| author | Qi, Lin Zhang, Jiaxin |
| author_facet | Qi, Lin Zhang, Jiaxin |
| contents | Fractals represent one of the fundamental manifestations of complexity, and fractal networks serve as tools for characterizing and investigating the fractal structures and properties of large-scale systems. Higher-order networks have emerged as a research hotspot due to their ability to express interactions among multiple nodes. This study proposes an iterative generation model for higher-order fractal networks. The iteration is controlled by three parameters: the dimension K of the simplicial complex, the multiplier m, and the iteration count t. The constructed network is a pure simplicial complex. Theoretical analysis using the similarity dimension and experimental verification using the box-counting dimension demonstrate that the generated networks exhibit fractal characteristics. When the multiplier m is large, the generalized degree distribution of the generated networks is characterized by its scale-free nature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Iterative Generation and Generalized Degree Distribution of Higher-Order Fractal Scale-Free Networks Qi, Lin Zhang, Jiaxin Combinatorics Fractals represent one of the fundamental manifestations of complexity, and fractal networks serve as tools for characterizing and investigating the fractal structures and properties of large-scale systems. Higher-order networks have emerged as a research hotspot due to their ability to express interactions among multiple nodes. This study proposes an iterative generation model for higher-order fractal networks. The iteration is controlled by three parameters: the dimension K of the simplicial complex, the multiplier m, and the iteration count t. The constructed network is a pure simplicial complex. Theoretical analysis using the similarity dimension and experimental verification using the box-counting dimension demonstrate that the generated networks exhibit fractal characteristics. When the multiplier m is large, the generalized degree distribution of the generated networks is characterized by its scale-free nature. |
| title | Iterative Generation and Generalized Degree Distribution of Higher-Order Fractal Scale-Free Networks |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.05869 |