Studying node centrality based on the hidden hyperbolic metric space of complex networks

Abstract With the hyperbolic model of the hidden metric space of networks, the hyperbolic DC of a node is defined, totally based on node features in the hyperbolic space but not directly related to network structures. The effectiveness of the hyperbolic DC in forecasting the true importance ranking of nodes in the network structure is studied. Simulations on the forecasting accuracy show it has a certain effectiveness in forecasting a few of the most important nodes, which provides possibility to carry out targeted attacks on networks without knowing any information of network structures. Moreover, for random attacks, a mechanism based on the hyperbolic DC is designed to enhance the destructive power, and the macro-matching degree is proposed to measure the effectiveness of the mechanism. Simulations show when parameter β is not big, the mechanism has quite good performance, and the smaller the value of β , the more effective the mechanism. Furthermore, for parameters in the hyperbolic model, their influences on the mechanism are researched. Results show temperature has more obvious influences than curvature, and the mechanism is found to become more effective when temperature becomes lower. According to the relationship between temperature and the clustering feature of the network, the research indicates our mechanism for random attacks should be effective for most real-world networks.

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