Robustness analysis of random hyper-networks based on the internal structure of hyper-edges

Bin Zhou; Xiujuan Ma; Fuxiang Ma; Shujie Gao; Bin Zhou; Xiujuan Ma; Fuxiang Ma; Shujie Gao

doi:10.3934/math.2023239

AIMS Mathematics

2023, Volume 8, Issue 2: 4814-4829. doi: 10.3934/math.2023239

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Robustness analysis of random hyper-networks based on the internal structure of hyper-edges

1.
School of Computer, Qinghai Normal University, Xining 810008, China
2.
The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Xining 810008, China

Received: 29 July 2022 Revised: 25 November 2022 Accepted: 29 November 2022 Published: 08 December 2022
MSC : 05C65, 28A80, 93B05

Random hyper-network is an important hyper-network structure. Studying the structure and properties of random hyper-networks, which helps researchers to understand the influence of the hyper-network structure on its properties. Currently, studies related to the influence of the internal structure of the hyper-edge on robustness have not been carried out for research on the robustness of hyper-networks. In this paper, we construct three $ k $-uniform random hyper-networks with different structures inside hyper-edges. The nodes inside hyper-edges are connected in the ways randomly connected, preferentially connected and completely connected. Meanwhile, we propose a capacity-load model that can describe the relationship between the internal structure and the robustness of the hyper-edge, based on the idea of capacity-load model. The robustness of the three hyper-networks was obtained by simulation experiments. The results show the variation of the internal structure of hyper-edge has a large influence on the robustness of the $ k $-uniform random hyper-network. In addition, the larger number of ordinary edges $ m_{k} $ inside the hyper-edges and the size of the hyper-network $ k $, the more robust the $ k $-uniform random hyper-network is.
- random hyper-networks,
- internal structure of hyper-edges,
- capacity-load model,
- cascading failures,
- robustness
Citation: Bin Zhou, Xiujuan Ma, Fuxiang Ma, Shujie Gao. Robustness analysis of random hyper-networks based on the internal structure of hyper-edges[J]. AIMS Mathematics, 2023, 8(2): 4814-4829. doi: 10.3934/math.2023239

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Abstract

Random hyper-network is an important hyper-network structure. Studying the structure and properties of random hyper-networks, which helps researchers to understand the influence of the hyper-network structure on its properties. Currently, studies related to the influence of the internal structure of the hyper-edge on robustness have not been carried out for research on the robustness of hyper-networks. In this paper, we construct three $ k $-uniform random hyper-networks with different structures inside hyper-edges. The nodes inside hyper-edges are connected in the ways randomly connected, preferentially connected and completely connected. Meanwhile, we propose a capacity-load model that can describe the relationship between the internal structure and the robustness of the hyper-edge, based on the idea of capacity-load model. The robustness of the three hyper-networks was obtained by simulation experiments. The results show the variation of the internal structure of hyper-edge has a large influence on the robustness of the $ k $-uniform random hyper-network. In addition, the larger number of ordinary edges $ m_{k} $ inside the hyper-edges and the size of the hyper-network $ k $, the more robust the $ k $-uniform random hyper-network is.

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