Node importance evaluation of multi-level directed weighted network based on ISM and SH combination model

The node in networks plays a different role in the structure and function, thus it is necessary to evaluate the importance of different nodes in the network. Now, the research on the importance of network nodes is mainly focused on undirected and unweighted networks. To accurately study the importance of nodes in directed and weighted networks, the importance of hierarchical division of network nodes and the constraint coefficient are considered from the macroscopic and microcosmic perspectives. In this paper, a new method to evaluate the influential nodes is proposed by a combination of interpretive structural model and the structural hole theory. The interpretive structural model can be used to classify the network nodes, which the higher the hierarchy, the more important the relative position of the node is in the network. The nodes’ network constraint coefficient reflects the possibility of forming structural holes in the networks, the smaller the constraint coefficient, the easier a node to form a structural hole, and nodes occupying the hole position of the structure are more important in the network. Firstly, dividing the hierarchies of the network nodes, and then calculating the network constraint coefficients of each node in the network, finally, this method is extended to be applied in the directed and weighted ARPA network to get the order of importance of each node. The combination model not only analyzes the network layer influence of the node, but also considers the association effect with the level of the node adjacent to the node. Therefore, the method can more accurately rank nodes in a directed weighted network.