Higher-order structure based node importance evaluation in directed networks

Evaluating the significance of objects with possible relevant information is a crucial topic in information science. Due to the fact that objects related to each other can often be described using complex networks, this topic also forms a fundamental theme in network science. Most traditional methods for characterizing the importance of nodes in complex networks only utilize the binary relationships between node pairs, neglecting the influence brought by higher-order structures. Considering the specific interaction modes between local nodes in the network, this paper associates the higher-order structural characteristics of the network with the importance of the nodes. It constructs an evaluation framework for the importance of nodes in directed networks based on higher-order structures. Experimental analysis on both artificial data and scientific citation data from the APS dataset has validated the effectiveness of the proposed algorithms. Compared with PageRank and eigenvector centrality, the proposed algorithms demonstrated higher accuracy, revealing the role of higher-order structures in node importance evaluation. Finally, a robustness analysis of several algorithms indicated that the proposed algorithms exhibited good robustness.