Article Details

Abstract

The identification of important nodes in higher-order networks is crucial for understanding network structural functions. To address the limitation of existing methods in capturing nodes' indirect influence in higher-order networks, this study proposes an improved node importance evaluation metric, EII2, based on multidimensional simplicial complex structures. This metric extends the Extended Influence Index (EII) by further incorporating second-order neighbor information of nodes within associated simplices, thereby providing a more comprehensive characterization of the node's influence propagation range in high-dimensional interactions. This study conducts simulation experiments on a constructed 4-dimensional random higher-order network (80 nodes and 400 simplices) and compares EII2 with EII and the Weighted Extended Influence Index (WEII). The experimental results show that under the same node-removal attack, the important node sequence identified by EII2 results in a steeper decline in the remaining network function S(q) , and particularly demonstrates better performance in the early attack stages. These results verify the effectiveness of EII2 in capturing higher-order correlations and improving the accuracy of important node identification.

Keywords

higher-order network; simplicial complex; important node identification; Extended Influence Index; second-order neighbor

References

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Funding

Research on the Robustness of Multi Layer Edge Coupled Dependent Systems (2025KYZ04)

About the authors

Nie Wen (1994-), male, Han ethnicity, from Jingzhou, Hubei, lecturer, master's student, research interests: machine learning, deep learning, algorithm analysis; Xie Yufeng (1997-), male, Han nationality, born in Jiujiang, Jiangxi, lecturer, master's student, research direction: modeling and analysis of complex network systems.