Tropospheric ozone (O3) time series have been converted into complex networks through the recent so-called Visibility Graph (VG), using the data from air quality stations located in the western part ...of Andalusia (Spain). The aim is to apply this novel method to differentiate the behavior between rural and urban regions when it comes to the ozone dynamics. To do so, some centrality parameters of the resulting complex networks have been investigated: the degree, betweenness and shortest path. Some of them are expected to corroborate previous works in order to support the use of this technique; while others to supply new information.
Results coincide when describing the difference that tropospheric ozone exhibits seasonally and geographically. It is seen that ozone behavior is fractal, in accordance to previous works. Also, it has been demonstrated that this methodology is able to characterize the divergence encountered between measurements in urban environments and countryside.
In addition to that, the promising outcomes of this technique support the use of complex networks for the study of air pollutants dynamics. Particularly, new nuances are offered such as the identification and description of singularities in the signal.
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Identifying influential nodes that lead to faster and wider spreading in complex networks is of theoretical and practical significance. The degree centrality method is very simple but of little ...relevance. Global metrics such as betweenness centrality and closeness centrality can better identify influential nodes, but are incapable to be applied in large-scale networks due to the computational complexity. In order to design an effective ranking method, we proposed a semi-local centrality measure as a tradeoff between the low-relevant degree centrality and other time-consuming measures. We use the Susceptible–Infected–Recovered (SIR) model to evaluate the performance by using the spreading rate and the number of infected nodes. Simulations on four real networks show that our method can well identify influential nodes.
► We propose a semi-local centrality measure to identify the influential nodes. ► Our method performs much better than well-known centrality indices. ► The computational complexity scales linearly with the network size. ► It is a better tradeoff of low-accurate and time-consuming measures.
The importance of researches on complex networks is becoming more and more prominent. How to identify influential nodes is still an urgent and crucial issue of many researches on complex networks. ...Many centrality measures, each has its own emphasis, have been put forward by researchers. Among them, centrality measures based on local properties of nodes are widely used, which assess the importance of nodes based on their degrees. However, they do not take the global information of networks into consideration. In this paper, a Local Degree Dimension (LDD) approach to identify influential nodes in complex networks is proposed. Different from the existing work, LDD regards the numbers of central node’s each layer neighbor nodes as the basis of nodes’ importance calculation. LDD creatively combines the increasing rate and decreasing rate of the numbers of each layer neighbor nodes to obtain its Local Degree Dimension value, which is comprehensive and reasonable. A node with a larger LDD value has a more significant impact on networks. To demonstrate the effectiveness of LDD, six experiments are conducted on six real-world complex networks. Experimental results show that LDD has a higher identification accuracy and a stronger ability to quantify node’s importance.
Ports, as the main components of global maritime transportation, have attracted attention from both industry and academia in relation to their safety management. Identifying the important ports of a ...maritime shipping network is necessary and significant for the recovery of ports when encountering severe disasters, especially with limited emergency resources. This paper proposes a new method to evaluate the importance of ports by incorporating centrality measures of networks into the TOPSIS framework. Three types of centrality measures were used in an integrated manner to provide a more comprehensive evaluation of the port importance. Some economic factors such as the throughput of ports and GDP of the cities are also considered in combination with the entropy weight method to determine the weight of each criterion in the proposed model. Furthermore, a case study of the ports along the (MSR) shipping network is conducted to demonstrate the feasibility and effectiveness of the proposed method in identifying essential ports.
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•This paper proposes a new method to evaluate the importance of ports by incorporating centrality measures and economic indicators (such as GDP and port throughput) into the TOPSIS framework.•This research provides a theoretical basis for identifying influential ports in complex maritime transportation networks.•The evaluation results revealed that among the top ten important ports of the MSR shipping network, six are from China. The top three most important ports are the Port of Singapore, Hong Kong and Shenzhen.
In complex networks, the nodes with most spreading ability are called influential nodes. In many applications such as viral marketing, identification of most influential nodes and ranking them based ...on their spreading ability is of vital importance. Closeness centrality is one of the most commonly used methods to identify influential spreaders in social networks. However, this method is time-consuming for dynamic large-scale networks and has high computational complexity. In this paper, we propose a novel ranking algorithm which improves closeness centrality by taking advantage of local structure of nodes and aims to decrease the computational complexity. In our proposed method, at first, a community detection algorithm is applied to extract community structures of the network. Thereafter, after ignoring the relationship between communities, one best node as local critical node for each community is extracted according to any centrality measure. Then, with the consideration of interconnection links between communities, another best node as gateway node is found. Finally, the nodes are sorted and ranked based on computing the sum of the shortest path length of nodes to obtained critical nodes. Our method can detect the most spreader nodes with high diffusion ability and low time complexity, which make it appropriately applicable to large-scale networks. Experiments on synthetic and real-world connected networks under common diffusion models demonstrate the effectiveness of our proposed method in comparison with other methods.
This paper examines the fundamental problem of identifying the most important nodes in a network. To date, more than a hundred centrality measures have been proposed, each evaluating the position of ...a node in a network from a different perspective. Our work focuses on PageRank which is one of the most important centrality measures in computer science used in a wide range of scientific applications. To build a theoretical foundation for choosing (or rejecting) PageRank in a specific setting, we propose to use an axiomatic approach. Specifically, we propose six simple properties and prove that PageRank is the only centrality measure that satisfies all of them. In this way, we provide the first axiomatic characterization of PageRank in its general form.
Identifying influential nodes in complex networks is still an open issue. Although various centrality measures have been proposed to address this problem, such as degree, betweenness, and closeness ...centralities, they all have some limitations. Recently, technique for order performance by similarity to ideal solution (TOPSIS), as a tradeoff between the existing metrics, has been proposed to rank nodes effectively and efficiently. It regards the centrality measures as the multi-attribute of the complex network and connects the multi-attribute to synthesize the evaluation of node importance of each node. However, each attribute plays an equally important part in this method, which is not reasonable. In this paper, we improve the method to ranking the node’s spreading ability. A new method, named as weighted technique for order performance by similarity to ideal solution (weighted TOPSIS) is proposed. In our method, we not only consider different centrality measures as the multi-attribute to the network, but also propose a new algorithm to calculate the weight of each attribute. To evaluate the performance of our method, we use the Susceptible–Infected–Recovered (SIR) model to do the simulation on four real networks. The experiments on four real networks show that the proposed method can rank the spreading ability of nodes more accurately than the original method.
•A weighted TOPSIS method for ranking node’s spreading ability is proposed.•To improve the original TOPSIS, a dynamically weighted algorithm is proposed.•Experimental results indicate that our method outperforms the classical method.
Identifying the influential spreaders in complex network has great theoretical and practical significance. In order to evaluate the spreading ability of the nodes, some centrality measures are ...usually computed, which include degree centrality (DC), betweenness centrality (BC), closeness centrality (CC), k-shell centrality (KS) and local centrality (LC). However, we observe that the performance of different centrality measures may change when these measures are used in a real network with different spreading probabilities. Specifically, DC performs well for small spreading probabilities and LC is more suitable for larger ones. To alleviate the sensitivity of these centrality measures to the spreading probability, we modify LC and then integrate it with DC by considering the spreading probability. We call the proposed measure hybrid degree centrality (HC). HC can take the advantages of DC or LC depending on the given spreading probability. We use SIR model to evaluate the performance of HC in both real networks and artificial networks. Experimental results show that HC performs robustly under different spreading probabilities. Compared with these known centrality measures such as DC, LC, BC, CC and KS, HC can evaluate the spreading ability of the nodes more accurately on most range of spreading probabilities. Furthermore, we show that our method can better distinguish the spreading ability of nodes.
•The common centralities are sensitive to the spreading probability.•A hybrid degree centrality is proposed to evaluate nodes’ spreading ability.•Our method integrates degree and local centrality with spreading probability.•Our method is not sensitive to the spreading probability.•Our method outperforms other centralities in both real and artificial networks.
Complex systems that consist of diverse kinds of entities that interact in different ways can be modeled by multilayer networks. This paper uses the tensor formalism with the Einstein product to ...model this type of networks. Several centrality measures, that are well known for single-layer networks, are extended to multilayer networks using tensors and their properties are investigated. In particular, subgraph centrality based on the exponential and resolvent of a tensor are considered. Krylov subspace methods based on the tensor format are introduced for computing approximations of different measures for large multilayer networks.
Ranking nodes by their spreading ability in complex networks is a fundamental problem which relates to wide applications. Local metric like degree centrality is simple but less effective. Global ...metrics such as betweenness and closeness centrality perform well in ranking nodes, but are of high computational complexity. Recently, to rank nodes effectively and efficiently, a semi-local centrality measure has been proposed as a tradeoff between local and global metrics. However, in semi-local centrality, only the number of the nearest and the next nearest neighbors of a node is taken into account, while the topological connections among the neighbors are neglected. In this paper, we propose a local structural centrality measure which considers both the number and the topological connections of the neighbors of a node. To evaluate the performance of our method, we use the Susceptible–Infected–Recovered (SIR) model to simulate the epidemic spreading process on both artificial and real networks. By measuring the rank correlation between the ranked list generated by simulation results and the ones generated by centrality measures, we show that our method can rank the spreading ability of nodes more accurately than centrality measures such as degree, k-shell, betweenness, closeness and local centrality. Further, we show that our method can better distinguish the spreading ability of nodes.
•The structure of the neighbors of a node can affect its spreading ability.•A local structural centrality method for ranking node’s spreading ability is proposed.•The proposed method considers both the number and structure of node’s neighbors.•The proposed method outperforms other measures on both real and artificial networks.•The proposed method is robust to different network sizes and community structure.
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