Abstract: Critical nodes in complex networks are generally more important than non-critical nodes. Existing methods to calculate the importance of nodes are mostly based on different measurement criteria. At present, in the case of less calculation methods for node criticality applicable to directed networks and less rigorous combination of different measurement indexes in the methods, a new method for calculating node criticality of directed network is proposed. The algorithm calculates the node key value by combining the node relation and the node position with the contribution matrix. The propagation experiment on the experimental network shows that, compared with the classical algorithm that evaluates the importance of key nodes by node degree centrality and other methods, this algorithm is more efficient in the process of mining key nodes, and the mined key nodes spread information more widely in the network.

Key words: directed network, contribution matrices, relational centrality, key node, influence propagation