# Multi-Attribute Decision Making Method for Node Importance Metric in Complex Network
## 5 Conclusions  
In this paper, we applied the CRITIC method to the process of node importance ranking, based on the H-index, closeness centrality, k-shell indicator, and network constraint coefficient, and a multi-attribute critic network decision indicator (MCNDI) was proposed to measure the node importance. The method takes into account not only the local neighborhood importance of the nodes but also combines the network location of the nodes with the amount of intermediate information, which makes the metric more generalizable. In the metric process, the CRITIC method is used to objectively determine the indicator weights based on the intrinsic nature of the data. Through metric measurement, we found that in the Chesapeake Bay network and contiguous USA network, the MCNDI evaluation results were less volatile and reflected the node importance more comprehensively compared to a single indicator. Then, we obtained the variation of network efficiency by simulating deliberate attack behavior in a real network based on different indicators. The simulation results show that the attack according to MCNDI was less dependent on the network topology and could maintain a stable evaluation performance, and the convergence rate of network efficiency was better than in other methods.  
The work in this paper is a further refinement of the node importance metric method and helps to expand the research ideas in the field of complex networks. At the same time, we also note that in networks with multi-layer structures covering more attributes such as weight, direction, time, and traffic, the method we provide is limited by the application conditions of the method, and the sub-indicators for multi-attribute decision making need to be improved to accommodate multi-dimensional network attributes. In recent years, exploring the importance ranking metrics of network nodes with more complex attribute conditions has also become an important research direction, which provides more ideas for our multi-attribute decision making. In this paper, we studied single-layer undirected unweighted networks, and the related methods can be extended to entitled networks [34], multiplexed networks [35], and other models that fit more closely to real networks. Additionally, the heterogeneity of nodes [36] puts new demands on importance ranking. In future work, we will continue to investigate node importance, in conjunction with the multilayer distribution structure of the network and the heterogeneity of the nodes.  
Conceptualization, Y.Z.; methodology, Y.L.; software, Y.Z.; validation, Y.Z.; writing--original draft preparation, Y.Z.; writing--review and editing, Y.Z., G.Y. and Z.H. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Not applicable. Not applicable. Not applicable. Data Availability Statement: Data available in a publicly accessible repository that does not issue DOIs Publicly available datasets were analyzed in this study. This data can be found here: [[http://konect.cc/networks/dimacs10-chesapeake/](http://konect.cc/networks/dimacs10-chesapeake/)]([http://konect.cc/networks/dimacs10-chesapeake/](http://konect.cc/networks/dimacs10-chesapeake/)), accessed on 21 December 2021; [[http://konect.cc/networks/contiguous-usa/](http://konect.cc/networks/contiguous-usa/)]([http://konect.cc/networks/contiguous-usa/](http://konect.cc/networks/contiguous-usa/)), accessed on 21 December 2021; [[https://networkrepository.com/inf-USAir97.php](https://networkrepository.com/inf-USAir97.php)]([https://networkrepository.com/inf-USAir97.php](https://networkrepository.com/inf-USAir97.php)), accessed on 21 December 2021; [[https://networkrepository.com/tech-routers-rf.php](https://networkrepository.com/tech-routers-rf.php)]([https://networkrepository.com/tech-routers-rf.php](https://networkrepository.com/tech-routers-rf.php)), accessed on 21 December 2021. The authors declare no conflict of interest.