Important hyperedge sorting method based on grounded Laplacian matrix

Abstract

How to use the methods of quantitative analysis to evaluate the importance of nodes or groups in complex networks is one of the important issues to be solved urgently in the field of network science research. Compared with the complex network, in which an edge represents the direct adjacent relationship between two nodes, the unique "hyperedge" in a hypernetwork is more suitable for representing groups, teams, and community structures of multiple nodes. Identifying the importance of teams and communities in the network is more conducive to controlling information dissemination in groups accurately, suppressing community-based outbreaks, predicting team research results, and discovering important drug targets. Existing algorithms focus on identifying important nodes in hypernetworks, and mining for important hyperedges is rare. In this paper, based on the hypergraph theory, combined with the property of the minimum eigenvalue of the grounded Laplacian matrix of the hypernetwork, a new index MEGL is proposed to identify the important hyperedges in hypernetwork. And it is applied in the drug target hypernetwork, which can not only identify important targets, but also identify important drugs. This method has important guiding significance for our drug development and target prediction, and also has certain reference significance for identifying important teams and communities in the network.