Key Nodes In Complex Networks Research Articles

Identification of key nodes in complex networks by using a joint technique of nonnegative matrix factorization and regularization

Identifying key nodes in complex networks is essential to deeply understand and fully utilize the properties and functions of complex systems. Currently, existing traditional methods perform critical nodes identification by manually selecting important attribute features of nodes, but there are limitations in this approach. Manual selection of attribute features may overlook non-obvious features related to nodes criticality and correlations between attribute features. To compensate for the shortcomings of traditional methods, a Joint Technique for identifying critical nodes, called JTNMFR, is presented based on Nonnegative Matrix Factorization and Regularization. Factorization of weighted adjacency matrix is performed to obtain potential attribute features of nodes, and communicability network matrix and similarity matrix are introduced as regularization terms to control sparsity of the decomposition results. Ultimately, the importance of nodes is assessed by constructing an objective function that integrates these two aspects and utilizing alternative iteration to obtain the attribute matrix. To validate the accuracy and reliability of JTNMFR, we compare it with nine other identification approaches on eight real networks. Experimental results show that JTNMFR not only significantly outperforms the other algorithms in terms of accuracy of node importance, monotonicity, and node spreading ability but also provides a more accurate means of assessing node importance.

Meta-path-based key node identification in heterogeneous networks

Identifying key nodes in complex networks remains challenging. Whereas previous studies focused on homogeneous networks, real-world systems comprise multiple node and edge types. We propose a meta-path-based key node identification (MKNI) method in heterogeneous networks to better capture complex interconnectivity. Considering that existing studies ignore the differences in propagation probabilities between nodes, MKNI leverages meta-paths to extract semantics and perform node embeddings. Trust probabilities reflecting propagation likelihoods are derived by calculating embedding similarities. Node importance is calculated by using metrics incorporating direct and indirect influence based on trust. The experimental results on three real-world network datasets, DBLP, ACM and Yelp, show that the key nodes identified by MKNI exhibit better information propagation in the Susceptible Infected (SI) and susceptibility-influence model (SIR) model compared to other methods. The proposed method provides a reliable tool for revealing the topological structure and functional mechanisms of the network, which can guide more effective regulation and utilization of the network.

A Novel Method to Identify Key Nodes in Complex Networks Based on Degree and Neighborhood Information

One key challenge within the domain of network science is accurately finding important nodes within a network. In recent years, researchers have proposed various node centrality indicators from different perspectives. However, many existing methods have their limitations. For instance, certain approaches lack a balance between time efficiency and accuracy, while the majority of research neglects the significance of local clustering coefficients, a crucial node property. Thus, this paper introduces a centrality metric called DNC (degree and neighborhood information centrality) that considers both node degree and local clustering coefficients. The combination of these two aspects provides DNC with the ability to create a more comprehensive measure of nodes’ local centrality. In addition, in order to obtain better performance in different networks, this paper sets a tunable parameter α to control the effect of neighbor information on the importance of nodes. Subsequently, the paper proceeds with a sequence of experiments, including connectivity tests, to validate the efficacy of DNC. The results of the experiments demonstrate that DNC captures more information and outperforms the other eight centrality metrics.

Identifying key nodes in complex networks based on an improved gravity model

The identification of key nodes in complex networks is a hot topic. Therefore, it attracts increasing attention from different fields, like airline networks and social networks. To identify the key nodes in complex network, we suggest an improved gravity model method that takes propagation features into account. Relevant experiments were carried out in four actual airline networks based on the Susceptible Infected Recovered (SIR) model. First, we analyze the correlation between the proposed method and other benchmark methods.Then, Kendall’s correlation coefficient and the imprecision function were used as evaluation metrics to analyze and validate the proposed method. Empirical results reveal that the suggested method outperforms previous benchmark methods in terms of precision and effectiveness for identifying key nodes, especially in the US air network, where Kendall’s tau achieves a 107% improvement compared to the gravity centrality method.

Identifying influential nodes in complex contagion mechanism

Identifying influential nodes in complex networks is one of the most important and challenging problems to help optimize the network structure, control the spread of the epidemic and accelerate the spread of information. In a complex network, the node with the strongest propagation capacity is known as the most influential node from the perspective of propagation. In recent years, identifying the key nodes in complex networks has received increasing attention. However, it is still a challenge to design a metric that has low computational complexity but can accurately identify important network nodes. Currently, many centrality metrics used to evaluate the influence capability of nodes cannot balance between high accuracy and low time complexity. Local centrality suffers from accuracy problems, while global metrics require higher time complexity, which is inefficient for large scale networks. In contrast, semi-local metrics are with higher accuracy and lower time cost. In this paper, we propose a new semi-local centrality measure for identifying influential nodes under complex contagion mechanisms. It uses the higher-order structure within the first and second-order neighborhoods of nodes to define the importance of nodes with near linear time complexity, which can be applied to large-scale networks. To verify the accuracy of the proposed metric, we simulated the disease propagation process in four real and two artificial networks using the SI model under complex propagation. The simulation results show that the proposed method can identify the nodes with the strongest propagation ability more effectively and accurately than other current node importance metrics.

Key nodes mining for complex networks based on local gravity model

Identification of key nodes in complex networks can effectively speed up the spread of favourable information or prevent the spread of rumours and diseases. An algorithm based on local gravity model is proposed to mine the key spreaders in complex networks. The existing algorithms based on gravity model consider the shortest distance between nodes. However, nodes not only influence each other through the shortest path, which will lead the loss of information between nodes. Different from the existing gravity model, the distance considered in this model is not the shortest distance between nodes, but the reciprocal of the number of feasible paths between nodes. Conveniently, the model is called FPLGM (Local Gravity Model Based on Feasible Paths). Ten different networks are utilised to verify the effectiveness of FPLGM. Results show that the FPLGM performs best in comparison with the well-known state-of-the-art methods.

Key Points-in-Time Identification of Gold Futures Market: A Complex Network Approach

Important nodes can determine the internal structure of complex networks and reveal the internal relationships of real-world systems, and identifying key nodes in complex networks is one of the important research areas of complex network science. As the king of commodities, changes in the price of gold significantly impact the economic development of various countries. Especially in the early stages of the outbreak of war between Russia and Ukraine, the price of gold futures has been greatly impacted, and the systemic risks are gradually spreading. In this paper, a gold future price series is mapped into a visibility graph (VG), the characteristics of the gold price time series and key points-in-time, have been explored from the perspective of complex network. First, according to the data structure characteristics of gold futures, this paper converts the closing prices of gold futures of the New York Mercantile Exchange into a complex network through the VG model. Then, by using the complex network model to further delve into the price of gold futures, it is found that the degree distribution of the gold futures network follows a power-law distribution, and has obvious scale-free characteristics. Finally, this paper uses the visual network node shrinking algorithm and the technique for order preference by similarity to ideal solution (TOPSIS) analysis method to identify the key nodes of the gold futures visual map to find the key time nodes in the timeline of gold futures market. Analysis of the key time nodes of this market by four methods reveals that the repetition rate of the key time nodes in the methods’ top 10 ranking is as high as 82.5%, indicating that the results obtained in this paper are robust. This study introduces a new model to describe the characteristics of gold futures price series, one which can find key time nodes in gold futures prices and provide potential help for predicting gold futures prices.

Identification of Key Nodes in Complex Networks Based on Network Representation Learning

Identification of Key Nodes in Complex Networks Based on Network Representation Learning

AOGC: An improved gravity centrality based on an adaptive truncation radius and omni-channel paths for identifying key nodes in complex networks

Identifying key nodes that have a significant impact on network structure and function is a fundamental issue with numerous practical applications and technical challenges. The gravity model is a unique method for identifying key nodes that has piqued the interest of many researchers. Most of existing gravity-based methods have limitations in that they neglect the surrounding environment of a node in deeper level such as node location, neighborhood topology, higher-order neighbors, multiple interaction paths, and so on. They assume that inter-node interactions occur only along the shortest path, which is not true and renders them inaccurate in many cases. Based on our defined adaptive truncation radius and “looseness distance” considering omni-channel paths, we propose a new gravity centrality method that integrates multiple node properties and accurately characterizes node interaction distance. Numerical simulations indicate that (i) the gravity model is a good approximation of node interaction effect and (ii) a derivative method outperforms recent high-performing node importance evaluation methods in terms of distinguishing ability, accuracy, spreading ability, and imprecision function with an acceptable time complexity. Furthermore, the proposed method exhibits good stability on networks of varying scales and structural characteristics.

Identifying Key Nodes in Complex Networks Based on Local Structural Entropy and Clustering Coefficient

Key nodes have a significant impact, both structural and functional, on complex networks. Commonly used methods for measuring the importance of nodes in complex networks are those using degree centrality, clustering coefficient, etc. Despite a wide range of application due to their simplicity, their limitations cannot be ignored. The methods based on degree centrality use only first-order relations of nodes, and the methods based on the clustering coefficient use the closeness of the neighbors of nodes while ignore the scale of numbers of neighbors. Local structural entropy, by replacing the node influence on networks with local structural influence, increases the identifying effect, but has a low accuracy in the case of high clustered networks. To identify key nodes in complex networks, a novel method, which considers both the influence and the closeness of neighbors and is based on local structural entropy and clustering coefficient, is proposed in this paper. The proposed method considers not only the information of the node itself, but also its neighbors. The simplicity and accuracy of measurement improve the significance of characterizing the reliability and destructiveness of large-scale networks. Demonstrations on constructed networks and real networks show that the proposed method outperforms other related approaches.

Analyzing the Characteristics and Evolution of Chinese Enterprises’ Outward Forward Direct Investment Host Country Network

With the promulgation of the “Going Global” strategy, Chinese enterprises’ outward forward direct investment (OFDI) moved towards a stage of rapid development. Based on the data concerning projects of Chinese enterprises, this paper establishes a network of OFDI host countries with the industry as the media and analyzes the network and its evolution characteristics by using the complex network method. Results show that the number of network nodes is increasing, and the edges between communities are greater, and the number of countries along the Belt and Road route is increasing. The network is a so-called small-world network. To reduce investment risks, it is necessary to identify the key nodes in the network. Based on the centrality of key nodes in complex networks, the improved “scatter degree” method is used to evaluate the importance of each host node. Results demonstrate that the United States and Australia are the most important countries for Chinese enterprises to invest overseas, followed by Brazil, Canada, Russia, Indonesia, and the United Kingdom (UK). Excluding the UK, all other countries are resource-rich. Thus, it can be seen that the FDI of Chinese enterprises is mainly resource-based investment.

Identifying Key Nodes in Complex Networks Based on Global Structure

Quantitative identification of key nodes in complex networks is of great significance for studying the robustness and vulnerability of complex networks. Although various centralities have been proposed to solve this issue, each approach has its limitations for its own perspective of determining an actor to be “key”. In this paper, we propose a novel method to identify key nodes in complex networks based on global structure. Three aspects including the shortest path length, the number of shortest paths and the number of non-shortest paths are considered, and we establish three corresponding influence matrices. Node efficiency, which can reflect the contribution of one node to the information transmission of the entire network, is selected as the initial value of node's influence on other nodes, and then the comprehensive influence matrix is constructed to reflect the influence among nodes. The proposed method provides a new measure to identify key nodes in complex networks from the perspective of global network structure, and can obtain more accurate identification results. Four experiments are conducted to evaluate the performance of our proposed method based on Susceptible-Infected (SI) model, and the results demonstrate the superiority of our method.

K-layer for Influencer Identification in Complex Networks

A small set of influential nodes, called influencers, spread information through a network faster and broader than other nodes. Identifying influencers has profound implications in various real-world spreading dynamics such as viral marketing, epidemic outbreaks and cascading failures. In this paper, we use and leverage the idea behind the widely-used k-shell index to introduce a new centrality index we call k-layer. The k-layer index, calculated through k-layer decomposition, quantifies the core of the network through the distance of nodes from the periphery of the network. Intuitively, the k-layer value of node i represents the depth of the node tree with node i as the root node within the scope of nodes that have been already removed. Our experimental results show that the proposed k-layer metric outperforms the k-shell index and the Mixed Degree Decomposition(MDD) in detecting the influencers of networks. After that, taking into account the node location characteristics in the network, an extended k-layer index, named KR-layer (KLR) is proposed and proved to have better ability to identify key nodes in complex networks. Our findings reveal the essential role of nodes’ distance from the periphery, leading us closer to the optimal solution of the influencer identification problem.

Multi-attribute ranking method for identifying key nodes in complex networks based on GRA

How to identify key nodes is a challenging and significant research issue in complex networks. Some existing evaluation indicators of node importance have the disadvantages of limited application scope and one-sided evaluation results. This paper takes advantage of multiple centrality measures comprehensively, by regarding the identification of key nodes as a multi-attribute decision making (MADM) problem. Firstly, a new local centrality (NLC) measure is put forward through considering multi-layer neighbor nodes and clustering coefficients. Secondly, combining the grey relational analysis (GRA) method and the susceptible-infectious-recovered (SIR) model, a modified dynamic weighted technique for order preference by similarity to ideal solution (TOPSIS) method is proposed. Finally, the effectiveness of the NLC is illustrated by applications to nine actual networks. Furthermore, the experimental results on four actual networks demonstrate that the proposed method can identify key nodes more accurately than the existing weighted TOPSIS method.

Identifying key nodes based on improved structural holes in complex networks

Identifying key nodes in complex networks is of theoretical and practical significance. Local metrics such as degree centrality is simplest but cannot effectively identify the important bridging nodes. Global metrics such as betweenness and closeness centrality can better identify important nodes, but they are often restricted by the unknown topology and cannot be conveniently applied in large-scale networks. In this paper, we propose an effective ranking method based on an Improved Structural Holes (ISH) to identify the important nodes. ISH method only uses the degree of nodes and the nearest neighborhood information rather than considering the global structure of a network. Our experimental results on five complex networks show that the proposed method can effectively identify the key nodes in complex networks and can also be applied in large-scale or unconnected networks.

A novel method of evaluating key nodes in complex networks

In order to evaluate the influence of nodes in complex networks, a new method is advanced of evaluating key nodes in complex networks, in combination with the “structural hole” theory and closeness centrality of nodes, through defining and applying the influence matrix of nodes’ “structural holes” in response to the limitations of existing methods. The “structural hole” theory gives a comprehensive consideration of the node degree as well as information about topological relations with its neighbors, whereas the closeness centrality of nodes is a reflection of the node's global information. The “structural holes” influence matrix in degree reflects the node's local and global information. So a more proper evaluation standard is established for influence of nodes and a simulation analysis is made of different-scale networks. The results of such analyses show that the method can not only make an exact assessment of the influence of nodes, but also obtain ideal evaluation results from actual complex networks of different scale.

Ranking key nodes in complex networks by considering structural holes

Structural hole nodes in complex networks play important roles in the network information diffusion. Unfortunately, most of the existing methods of ranking key nodes do not integrate structural hole nodes and other key nodes. According to the relevant research on structural hole theory as well as the key node ranking methods, network constraint coefficient, betweenness centrality, hierarchy, efficiently, network size, PageRank and clustering coefficient, 7 metrics are selected to rank the key nodes. Based on the 7 metrics, a ranking learning method based on ListNet is introduced to solve ranking key nodes by multi metrics. Comprehensive experiments are conducted based on different artificial networks and real complex networks. Experimental results with manual annotation show that the ranking method can comprehensively consider the structural hole nodes and other nodes with different important features. The ranking results on different networks are highly consistent with the manual ranking results. The spreading experiment results using signed to interference ratio propagation model show that SIR model can reach a maximum propagating ratio in a shorter propagating time initiated by TOP-K key nodes selected by our method than TOP-K key nodes selected by other methods.

A new clustering algorithm based on data field in complex networks

The evaluation of node importance in complex networks has been an increasing widespread concern in recent years. Seeking and protecting vital nodes is important to ensure the security and stability of the whole network. Existing clustering algorithms of complex networks all have certain drawbacks, which could not cover everything in calculation accuracy and time complexity, and need external supervision. To design a fast complex networks clustering method is a problem which requires to be solved immediately. This paper proposes a clustering algorithm of complex networks based on data field using physical data field theory, which excavates key nodes in complex networks by evaluating the importance of nodes based on a mutual information algorithm, and then uses it to classify the clusters. To verify the validity of the algorithm, a simulation experiment was conducted. The results indicated that the algorithm could analyze the cluster exactly and calculate with high-speed, it could also determine the granularity of a partition according to the actual demand.

Key nodes in complex networks identified by multi-attribute decision-making method

In complex networks, it is significant how to rank the nodes according to their importance. Most of the existing methods of ranking key nodes (e.g. degree-based, betweenness-based) only consider one factor but not the integration of whole complex network in evaluating the importance of nodes, so those methods each have a limited application range. In this paper, a multi-attribute decision-making method to identify the key nodes in complex networks is proposed. In our method, each node is regarded as a solution, and each importance evaluation criterion as one solution's attribute. After that, we calculate the closeness between each solution and the ideal solution in order to obtain the integration results of node importance in complex networks. The proposed method can be used in a variety of complex networks. It is also easy to evaluate the importance evaluation criteria. Finally, experimental results show that the proposed method is effective.

Transforming a complex network to an acyclic one

Acyclic networks are a class of complex networks in which links are directed and do not have closed loops. Here we present an algorithm for transforming an ordinary undirected complex network into an acyclic one. Further analysis of an acyclic network allows one to find the structural properties of the network. With our approach one can find the communities and key nodes in complex networks. Also we propose a new parameter of complex networks which can mark the most vulnerable nodes of the system. The proposed algorithm can be applied to finding communities and bottlenecks in general complex networks.