# Identifying and Ranking Influential Nodes in Complex Networks Based on Dynamic Node Strength
## 4 Conclusions  
In this paper, we propose an efficient ranking method based on decomposing networks, Dynamic Node Strength Decomposition, to identify and rank the node influence in complex networks. The effect of decomposition process on ranking result is reflected by dynamic degree, which is evaluated the degree vanished in the decomposing process and the existing degree [25]. The spreading paths are distinguished by the dynamic degree of nodes at  
Figure 5: The [PERSON]’s \(\tau\) between the rankings obtained by different methods and the spreading capacity simulated by the SIR model: \(\alpha\) is set to 0.5 and \(\beta\) is set to 0 (**a–d**); the \(\tau\) of DNSD with \(\alpha\) set between 0.3 and 0.7 with an an interval of 0.1 (**e–h**); and the \(\tau\) of DNSD\({}^{+}\) with \(\alpha\) set between 0.3 and 0.7 with an an interval of 0.1 (**i–l**).  
Figure 6: The Kendall’s \(\tau\) between the rankings obtained by our methods and node influence simulated by the SIR model: (**a–d**) measured by DNSD; and (**e–h**) measured by DNSD\({}^{+}\). \(\alpha\) is set to 0.5. \(\beta\) is set to 0–1 with the interval 0.1.  
both ends of edge, and dynamic node strength is composed of edge weight of nodes and neighbors. Our methods have better monotonic than degree centrality, k-shell, MDD and C\({}_{\rm nc}\) by monotonicity index. We evaluated the effectiveness of ranking methods by Kendall's \(\tau\) of the ranking obtained by the ranking methods and the size of infected scale of SIR simulation. The experimental results show that the ranking result of our method are highly correlated with the spreading capacity simulated by SIR. We can draw the conclusion that the proposed methods are better than degree centrality, k-shell, MDD and C\({}_{\rm nc}\) methods in the specific types of networks, such as email, co-authors and power grid networks [31], when SIR simulation is applied.  
Our methods still have much room for improvement in some way. Some works show that the influence of nodes cloud be affected by the size of their community [42; 43]. As long as neighbors considered are wide enough, there is not much deviation between rank measured by our method and real influence of node. This is not advisable because of the large amount of calculation. Moreover, finding the set of influential spreaders in complex networks is something our method cannot deal with [44; 45], where node influence, the distance between nodes in the influential set and size of influential set need to be considered. Therefore, some more effective and efficient improvements will still be sought in further investigation.  
Conceptualization, X.L. and Q.S.; methodology, X.L. and Q.S.; software, X.L.; validation, X.L.; formal analysis, X.L. and Q.S.; investigation, X.L. and Q.S.,resources, X.L. and Q.S.; writing--original draft preparation, X.L.; writing--review and editing, X.L. and Q.S.; visualization, X.L.; supervision, Q.S.; project administration, Q.S.; and funding acquisition, Q.S. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Beijing Social Science Fund No. 11 JGB063. and Social Science Research Project of Ministry of Education No. 11 YJA630109.  
The authors declare no conflict of interest.