Study on the reliability of hypergraphs based on non-backtracking matrix centrality

Abstract

In recent years, there has been widespread attention on hypergraphs as a research hotspot in network science.The unique structure of hypergraphs, which differs from traditional graphs, is characterized by hyperedges that can connect multiple nodes simultaneously, resulting in more complex and higher-order relationships.Effectively identifying important nodes and hyperedges in such network structures poses a key challenge.Eigenvector centrality, a common metric, has limitations in its application due to its locality when dealing with hub nodes with extremely high degree values in the network.To address this issue, the hypergraphs were transformed into their corresponding line graphs, and non-backtracking matrix centrality was employed as a method to measure the importance of hyperedges.This approach demonstrated better uniformity and differentiation in assessing the importance of hyperedges.Furthermore, the application of both eigenvector centrality and non-backtracking matrix centrality in assessing the importance of nodes in hypergraphs was explored.Comparative analysis revealed that non-backtracking matrix centrality effectively distinguished the importance of nodes.This research encompassed theoretical analysis, model construction, and empirical studies on real-world data.To validate the proposed method and conclusion, six real-world hypergraphs were selected as experimental subjects.The application of these methods to these hypergraphs confirmed the effectiveness of non-backtracking matrix centrality in identifying important nodes and hyperedges.The findings of this research offer a fresh perspective and approach for identifying key elements in hypergraphs, holding significant theoretical and practical implications for understanding and analyzing complex network systems.

Keywords

• hypergraph
• eigenvector centrality
• non-backtracking matrix centrality
• vector centrality