A Generative Hypergraph Model for Double Heterogeneity
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916531340836864 |
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| author | Li, Zhao Zhang, Jing Zhang, Jiqiang Zheng, Guozhong Cai, Weiran Chen, Li |
| author_facet | Li, Zhao Zhang, Jing Zhang, Jiqiang Zheng, Guozhong Cai, Weiran Chen, Li |
| contents | While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect more than two nodes, have thus become a new paradigm in network science. Yet, we are still in lack of models linking network growth and hyperedge expansion, both of which are commonly observable in the real world. Here, we propose a generative hypergraph model by employing the preferential attachment mechanism in both nodes and hyperedge formation. The model can produce bi-heterogeneity, exhibiting scale-free distributions in both hyperdegree and hyperedge size. We provide a mean-field treatment that gives the expression of the two scaling exponents, which agree with the numerical simulations. Our model may help to understand the networked systems showing both types of heterogeneity and facilitate the study of complex dynamics thereon. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_13977 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Generative Hypergraph Model for Double Heterogeneity Li, Zhao Zhang, Jing Zhang, Jiqiang Zheng, Guozhong Cai, Weiran Chen, Li Physics and Society Disordered Systems and Neural Networks Adaptation and Self-Organizing Systems While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect more than two nodes, have thus become a new paradigm in network science. Yet, we are still in lack of models linking network growth and hyperedge expansion, both of which are commonly observable in the real world. Here, we propose a generative hypergraph model by employing the preferential attachment mechanism in both nodes and hyperedge formation. The model can produce bi-heterogeneity, exhibiting scale-free distributions in both hyperdegree and hyperedge size. We provide a mean-field treatment that gives the expression of the two scaling exponents, which agree with the numerical simulations. Our model may help to understand the networked systems showing both types of heterogeneity and facilitate the study of complex dynamics thereon. |
| title | A Generative Hypergraph Model for Double Heterogeneity |
| topic | Physics and Society Disordered Systems and Neural Networks Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2306.13977 |