No abstract

Identifying vital nodes is a significant issue for the study of network robustness, epidemic controlling and targeted destruction of networks. Previous studies on weak ties theory recovered that ties with weak strength usually act as the important bridges that connect different clusters and play important role in maintaining the network connectivity. In this paper, we quantify the strength of links based on local information of the network topology, and design a simple yet effective method to evaluate nodes' importance in terms of the number of their connections and overlap of their neighbors. Experimental analyses on synthetic and real networks demonstrate that the proposed algorithm identifies vital nodes leading to faster network collapse in target destruction than some well-known methods.

Ranking node importance is of great significance for studying the robustness and vulnerability of complex network. Over the recent years, various centrality indices such as degree, semilocal, K-shell, betweenness and closeness centrality have been employed to measure node importance in the network. Among them, some well-known global measures such as betweenness centrality and closeness centrality can achieve generally higher accuracy in ranking nodes, while their computation complexity is relatively high, and also the global information is not readily available in a large-scaled network. In this paper, we propose a new local metric which only needs to obtain the neighborhood information within two hops of the node to rank node importance. Firstly, we calculate the similarity of node neighbors by quantifying the overlap of their topological structures with Jaccard index; secondly, the similarity between pairs of neighbor nodes is calculated synthetically, and the redundancy of the local link of nodes is obtained. Finally, by reducing the influence of densely local links on ranking node importance, a new local index named LLS that considers both neighborhood similarity and node degree is proposed. To check the effectiveness of the proposed method of ranking node importance, we carry out it on six real world networks and one artificial small-world network by static attacks and dynamic attacks. In the static attack mode, the ranking value of each node is the same as that in the original network. In the dynamic attack mode, once the nodes are removed, the centrality of each node needs recalculating. The relative size of the giant component and the network efficiency are used for network connectivity assessment during the attack. A faster decrease in the size of the giant component and a faster decay of network efficiency indicate a more effective attack strategy. By comparing the decline rates of these two indices to evaluate the connectedness of all networks, we find that the proposed method is more efficient than traditional local metrics such as degree centrality, semilocal centrality, K-shell decomposition method, no matter whether it is in the static or dynamic manner. And for a certain ranking method, the results of the dynamic attack are always better than those of the static attack. This work can shed some light on how the local densely connections affect the node centrality in maintaining network robustness.

Identifying critical nodes in complex networks has gained increasing attention in recent years. However, how to design an algorithm that has low computational complexity but can accurately identify important network nodes is still a challenge. Considering the role of structural holes in shaping communication channels, this paper presents an effective method based on local characteristics to identify critical nodes that play important roles in maintaining network connectivity. Our method considers the connections of a node as well as the connectivity of the neighborhood of the node. Through numerical simulations on various real-world networks, we have demonstrated that the proposed approach outperforms some other well-known heuristic algorithms in identifying vital nodes and leads to faster network collapse in target destruction.

How to use quantitative analysis methods to identify which nodes are the most important in complex network, or to evaluate the importance of a node relative to one or more other nodes, is one of the hot issues in network science research. At present, a variety of effective models have been proposed to identify important nodes in complex network. Among them, the gravity model regards the coreness of nodes as the mass of nodes, the shortest distance between nodes as the distance between objects, and comprehensively considers the local information of nodes and path information to identify influential nodes. However, only the coreness is use to represented as the quality of the object, and the factors considered are relatively simple. At the same time, some studies have shown that the network can easily identify the core-like group nodes with local high clustering characteristics as core nodes when performing k-core decomposition,which leads to the inaccuracy of the gravity algorithm. Based on the universal gravitation method, considering the node h index, the number of node cores and the location of node structural holes, this paper proposes an improved algorithm ISM and its extended algorithm ISM₊. The SIR model is used to simulate the propagation process on several classical real networks and artificial networks, and the results show that the proposed algorithm can better identify important nodes in the network than other centrality indicators.