Exploring growing complex systems with higher-order interactions

Soo Min Oh; Yongsun Lee; Byungnam Kahng

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arXiv · 2410.06279

Exploring growing complex systems with higher-order interactions

Soo Min Oh·Yongsun Lee·Byungnam Kahng

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Abstract

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.

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Soo Min Oh, Yongsun Lee, Byungnam Kahng. 2024-10-08. Exploring growing complex systems with higher-order interactions. https://arxiv.org/abs/2410.06279

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