A new model to identify node importance in complex networks based on DEMATEL method

Wentao Fan,Xiao Han,Yuhuan He,Yancheng Feng

doi:10.1038/s41598-021-02306-y

Abstract

It is still a hot research topic to identify node importance in complex networks. Recently many methods have been proposed to deal with this problem. However, most of the methods only focus on local or path information, they do not combine local and global information well. In this paper, a new model to identify node importance based on Decision-making Trial and Evaluation Laboratory (DEMATEL) is presented. DEMATEL method is based on graph theory which takes the global information into full consideration so that it can effectively identify the importance of one element in the whole complex system. Some experiments based on susceptible-infected (SI) model are used to compare the new model with other methods. The applications in three different networks illustrate the effectiveness of the new model.

Highlights

It is still a hot research topic to identify node importance in complex networks
Some methods to identify node importance have already been proposed such as degree centrality (DC)[8,9] betweenness centrality (BC)[10,11], closeness centrality (CC)[10], eigenvector centrality (EC)[12] and so o n13–16
The weight of each node is calculated by the normalized largest eigenvector.20proposed that the location of principal eigenvector (PEV) and the delocalization of principal eigenvector will cause difficulties when ranking nodes based on EC which means that EC is not suitable for the networks with delocalized PEV

Summary

Proposed method

A wide variety of node centrality measurements have been proposed these years. Each has its own advantages and disadvantages. The Gravity model considers both local and path information. Based on DEMATEL method, the indirect influence in the network is well addressed, making the new model more globally than the Gravity model. In Gravity model, node degree represents local information and distance represents path information. The normalized relation matrix continues to multiply in order to add indirect influence between all nodes in complex networks. Step 6 Calculate the causal parameters R and C based on total relation matrix (21). The novelty is that the new model considers indirect influence among nodes based on DEMATEL method and takes it as global information to enhance the effectiveness. The new proposed method weighted gravity model is improved based gravity model from a global perspective, but the global information is gained from the eigenvector of the adjacency matrix.

Networks n m k d

BC DC CC EC Gravity WGravity DGravity

Conclusion

Additional information