Exploring growing complex systems with higher-order interactions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916475438104576 |
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| author | Oh, Soo Min Lee, Yongsun Kahng, Byungnam |
| author_facet | Oh, Soo Min Lee, Yongsun Kahng, Byungnam |
| contents | A complex system with many interacting individuals can be represented by a network consisting of nodes and links representing individuals and pairwise interactions, respectively. However, real-world systems grow with time and include many higher-order interactions. Such systems with higher-order interactions can be well described by a simplicial complex (SC), which is a type of hypergraph, consisting of simplexes representing sets of multiple interacting nodes. Here, capturing the properties of growing real-world systems, we propose a growing random SC (GRSC) model where a node is added and a higher dimensional simplex is established among nodes at each time step. We then rigorously derive various percolation properties in the GRSC. Finally, we confirm that the system exhibits an infinite-order phase transition as higher-order interactions accelerate the growth of the system and result in the advanced emergence of a giant cluster. This work can pave the way for interpreting growing complex systems with higher-order interactions such as social, biological, brain, and technological systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06279 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploring growing complex systems with higher-order interactions Oh, Soo Min Lee, Yongsun Kahng, Byungnam Physics and Society Statistical Mechanics A complex system with many interacting individuals can be represented by a network consisting of nodes and links representing individuals and pairwise interactions, respectively. However, real-world systems grow with time and include many higher-order interactions. Such systems with higher-order interactions can be well described by a simplicial complex (SC), which is a type of hypergraph, consisting of simplexes representing sets of multiple interacting nodes. Here, capturing the properties of growing real-world systems, we propose a growing random SC (GRSC) model where a node is added and a higher dimensional simplex is established among nodes at each time step. We then rigorously derive various percolation properties in the GRSC. Finally, we confirm that the system exhibits an infinite-order phase transition as higher-order interactions accelerate the growth of the system and result in the advanced emergence of a giant cluster. This work can pave the way for interpreting growing complex systems with higher-order interactions such as social, biological, brain, and technological systems. |
| title | Exploring growing complex systems with higher-order interactions |
| topic | Physics and Society Statistical Mechanics |
| url | https://arxiv.org/abs/2410.06279 |