# Identifying and Ranking Influential Nodes in Complex Networks Based on Dynamic Node Strength
## 1 Introduction  
Spreading phenomenon generally exists in various fields including physics [1], ecology [2], biology [3] and so on, which is studied in the framework of complex network appropriately. Identifying and ranking the influential spreaders in the complex network is significant for understanding the spreading mechanism. Many works focus on how to measure the influence of nodes in a sufficiently large and complex network [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]. As is known, there are numerous classic topology metrics, including degree centrality [12], betweenness centrality [13], closeness centrality [14], Katz centrality [15] and so on, which can be adopted to distinguish which nodes are more important. However, the methods of ranking influential nodes are constantly improved.  
In recent years, various efficient ranking methods to identify influential nodes in the complex network are proposed, such as LeaderRank [16], PageRank [17], semi-local centrality [18], TOPSIS [19, 20], HybridRank [21] and so on. Among these methods, the k-shell method proposed by [PERSON] et al. [22] is the most well-known. It has been found that the location of spreader has a great impact on spreading, and the most influential spreaders are often located in the core of the network. Based on this feature, they proposed the method named k-shell to decompose network according to degree. In this method, each node is assigned to an index \(k_{s}\) and nodes with large \(k_{s}\) are influential. There is an obvious drawback of decomposing networks according to the classical k-shell method: too many nodes are assigned to the same rank which leads to the coarse ranking. This is caused by a variety of factors: First, the standard for a node to be removed is only its degree, which does not take local influence of its neighbors into account [23]. Second, the process of removing nodes is recursive, and the order of nodes removed will affect the ranking result. Third, the global characteristics of the network are considered insufficiently [24].  
The idea of ranking influential spreaders based on decomposing network is desirable because this kind of method generally has low computational complexity. The processof decomposing networks could be regarded as the recurrence of spreading process in some sense [25]. [PERSON] et al. [26] presented that the locations of node neighbors should not be ignored and proposed a novel method based on decomposing networks, coreness centrality (C\({}_{\text{nc}}\)), to evaluate spreading capability of a node by considering the coreness of its neighbors. [PERSON] et al. [25] considered the residual edges when decomposing the network, whereas the information contained in the exhausted nodes and edges is ignored, and proposed the mixed degree decomposition (MDD) to consider both the residual degree and the exhausted degree. [PERSON] et al. [27] proposed a method to generate a more distinguishable ranking list based on distance from the target node to the core of network. [PERSON] et al. [28] utilized neighborhood attributes and entropy method to weight the node position based on iteration information in the k-shell decomposition. Overall, decomposing networks to identify the node influence is advisable.  
Based on decomposing networks dynamically, we propose a method named Dynamic Node Strength Decomposition (DNSD) to identify and rank node influence: both the difference of edges and the influence of decomposition order on the node ranking are also taken into account. To evaluate the effectiveness of the proposed method, we apply the Susceptible-Infected-Recovered (SIR) model to simulate spreading process in four real networks and measure the Kendall's \(\tau\) between the ranking and spreading capacity of nodes. Experimental results show that our method has good advantage in resolution ratio and performs more effective in identifying influential spreaders than other methods.