A Node Importance Measuring Method based on Hypernetwork

Measuring the importance of nodes in network is an important issue in the study of complex networks. The networks in current researches are mostly based on classical graph theory, which have limitations on describing certain complex relations. In this work, we introduce hypernetwork, taking hypergraph as representation foundation, to describe relations. Hypernetwork is able to extend the modeling and describing capability of traditional network and may be a promising representation model of complex relations. However, a general lack of attention to the node importance measuring in hypernetwork, an important fundamental issue for its further application, has been noted across the majority of related published works. In this paper, we utilize the idea of deleting method, to measure the importance of node in hypernetwork through investigating the influence on the whole network when deleting it. Specifically, the influence is measured by direct loss and indirect loss. Through a calculating example, our method is compared with node degree, betweenness, closeness centrality, degree of neighbor nodes etc., the result shows this method has better adaptability and accuracy.