Node Importance In Complex Networks Research Articles

Excavating important nodes in complex networks based on the heat conduction model

Analyzing the important nodes of complex systems by complex network theory can effectively solve the scientific bottlenecks in various aspects of these systems, and how to excavate important nodes has become a hot topic in complex network research. This paper proposes an algorithm for excavating important nodes based on the heat conduction model (HCM), which measures the importance of nodes by their output capacity. The number and importance of a node’s neighbors are first used to determine its own capacity, its output capacity is then calculated based on the HCM while considering the network density, distance between nodes, and degree density of other nodes. The importance of the node is finally measured by the magnitude of the output capacity. The similarity experiments of node importance, sorting and comparison experiments of important nodes, and capability experiments of multi-node infection are conducted in nine real networks using the Susceptible-Infected-Removed model as the evaluation criteria. Further, capability experiments of multi-node infection are conducted using the Independent cascade model. The effectiveness of the HCM is demonstrated through a comparison with eight other algorithms for excavating important nodes.

Dynamic identification of important nodes in complex networks based on the KPDN–INCC method

This article focuses on the cascading failure problem and node importance evaluation method in complex networks. To address the issue of identifying important nodes in dynamic networks, the method used in static networks is introduced and the necessity of re-evaluating node status during node removal is proposed. Studies have found that the methods for identifying dynamic and static network nodes are two different directions, and most literature only uses dynamic methods to verify static methods. Therefore, it is necessary to find suitable node evaluation methods for dynamic networks. Based on this, this article proposes a method that integrates local and global correlation properties. In terms of global features, we introduce an improved k-shell method with fusion degree to improve the resolution of node ranking. In terms of local features, we introduce Solton factor and structure hole factor improved by INCC (improved network constraint coefficient), which effectively improves the algorithm’s ability to identify the relationship between adjacent nodes. Through comparison with existing methods, it is found that the KPDN–INCC method proposed in this paper complements the KPDN method and can accurately identify important nodes, thereby helping to quickly disintegrate the network. Finally, the effectiveness of the proposed method in identifying important nodes in a small-world network with a random parameter less than 0.4 was verified through artificial network experiments.

Dynamic identification of important nodes in complex networks by considering local and global characteristics

Abstract By combining centrality measures and community detection, a better insight into the nature of the evolution of important nodes in complex networks is obtained. Meanwhile, the dynamic identification of important nodes in complex networks can be enhanced by considering both local and global characteristics. Local characteristics focus on the immediate connections and interactions of a node within its neighbourhood, while global characteristics take into account the overall structure and dynamics of the entire network. Nodes with high local centrality in dynamic networks may play crucial roles in local information spreading or influence. On the global level, community detection algorithms have a significant impact on the overall network structure and connectivity between important nodes. Hence, integrating both local and global characteristics offers a more comprehensive understanding of how nodes dynamically contribute to the functioning of complex networks. For more comprehensive analysis of complex networks, this article identifies important nodes by considering local and global characteristics (INLGC). For local characteristic, INLGC develops a centrality measure based on network constraint coefficient, which can provide a better understanding of the relationship between neighbouring nodes. For global characteristic, INLGC develops a community detection method to improve the resolution of ranking important nodes. Extensive experiments have been conducted on several real-world datasets and various performance metrics have been evaluated based on the susceptible–infected–recovered model. The simulation results show that INLGC provides more competitive advantages in precision and resolution.

Identifying critical nodes in complex networks based on neighborhood information

The identification of important nodes in complex networks has always been a prominent topic in the field of network science. Nowadays, the emergence of large-scale networks has sparked our research interest in complex network centrality methods that balance accuracy and efficiency. Therefore, this paper proposes a novel centrality method called Spon (Sum of the Proportion of Neighbors) Centrality, which combines algorithmic efficiency and accuracy. Spon only requires information within the three-hop neighborhood of a node to assess its centrality, thereby exhibiting lower time complexity and suitability for large-scale networks. To evaluate the performance of Spon, we conducted connectivity tests on 16 empirical unweighted networks and compared the monotonicity and algorithmic efficiency of Spon with other methods. Experimental results demonstrate that Spon achieves both accuracy and algorithmic efficiency, outperforming eight other methods, including CycleRatio, collective influence, and Social Capital. Additionally, we present a method called W-Spon to extend Spon to weighted networks. Comparative experimental results on 10 empirical weighted networks illustrate that W-Spon also possesses advantages compared to methods such as I-Core and M-Core.

Node importance measurement method based on multi-attribute fusion

Finding important nodes in complex networks is an important topic. However, the location information obtained by many previous studies is not sufficient and effective, and the types of attributes applied also have limitations. Based on K-shell and gravity model, this paper proposes a node importance measurement method based on multi-attribute fusion. In this method, the objective, comprehensive evaluation of multiple attributes is obtained by the entropy weight method. Experiments on real networks show that the proposed algorithm can effectively measure the importance of nodes.

Identifying important nodes in complex networks based on extended degree and E-shell hierarchy decomposition

The identification of important nodes is a hot topic in complex networks. Many methods have been proposed in different fields for solving this problem. Most previous work emphasized the role of a single feature and, as a result, rarely made full use of multiple items. This paper proposes a new method that utilizes multiple characteristics of nodes for the evaluation of their importance. First, an extended degree is defined to improve the classical degree. And E-shell hierarchy decomposition is put forward for determining nodes’ position through the network’s hierarchical structure. Then, based on the combination of these two components, a hybrid characteristic centrality and its extended version are proposed for evaluating the importance of nodes. Extensive experiments are conducted in six real networks, and the susceptible–infected–recovered model and monotonicity criterion are introduced to test the performance of the new approach. The comparison results demonstrate that the proposed new approach exposes more competitive advantages in both accuracy and resolution compared to the other five approaches.

A new scheme for identifying important nodes in complex networks based on generalized degree

The identification of important nodes is a fundamental problem of complex networks. To address this issue, the k-shell decomposition algorithm and its improvements has been presented. The classical K-shell algorithm fails to provide the promising results in practical situations because of the resolution and performance problems. Therefore, this paper proposes a new scheme named generalized degree decomposition (GDD) algorithm for the identification of important nodes. In our scheme, first, each edge is assigned with hidden weight to describe its potential contribution to the network. Then, the generalized degree of each node is calculated based on the weights of the edges connected the node and its neighbors. At last, each node is attached with a corresponding index according to its stripping stage in the network pruning process. A large number of experiments are performed in eight real networks, and the findings demonstrate that the proposed scheme optimizes the performance and resolution.

Research on node influence in complex network based on multi-scale centrality algorithm

In network information mining, people must measure the influence of important nodes in complex networks, otherwise it cannot be mined. However, traditional node influence measurement methods have defects and strong application limitations. Therefore, this paper proposes a multi-scale centrality algorithm under some traditional methods, and carries out related research. This paper introduces the basic concept and application advantages of multi-scale centrality algorithm, then constructs the algorithm model, and finally verifies the effectiveness of the algorithm model in the measurement of node influence in complex networks. After verification, the algorithm is effective and the measurement result is accurate.

Identification of Important Nodes in Multilayer Heterogeneous Networks Incorporating Multirelational Information

Centrality is an effective method to identify important nodes in complex networks, but it is still a challenge to find influential nodes by making full use of multiple relationships and global network topological features in complex networks. To address these problems, this article proposes an importance identification method for multilayer heterogeneous network node by incorporating multirelational information (MLC). This method studies the relational characteristics of heterogeneous nodes in detail and divides the heterogeneous nodes into different layers according to the node types, which can be further divided into core and auxiliary layers. The importance of the auxiliary layer is quantified by designing the interlayer influence and determining the interlayer influence weights of different connectivity influences; the centrality score of heterogeneous nodes under multiconnectivity relationships is fused using the transmission characteristics of internode relationships in the auxiliary layer, which in turn measures the importance of nodes in the core layer. To evaluate the proposed algorithm, we conduct experiments on five real multilayer heterogeneous networks of different sizes. The results show that MLC can make full use of different types of internode association relationship information, effectively fuse network structure information such as the neighbor weights of core and auxiliary layer nodes, and outperform the existing techniques in identifying important nodes.

Node influence ranking in complex networks: A local structure entropy approach

The mining of important nodes in complex networks is a topic of immense interest due to its wide applications across many disciplines. In this paper, a Local Structure Entropy (LSE) approach is proposed based on the Taslli entropy by removing nodes, and by considering the information of the first-order and second-order neighboring nodes, in order to explore the impact of removing nodes on the network structure. With this method, the degree and betweenness of the first-order and second-order adjacent nodes are combined by Taslli entropy, and the influential nodes are measured by the structural characteristics of the network after nodes removal. To verify the effectiveness of LSE, we compare our method with five existing methods and perform experiments on seven real-world networks. The experimental results indicate that the influential nodes identified by LSE are better than the existing methods in terms of the range of information dissemination and robustness. Moreover, it is negatively correlated with closeness centrality and the PageRank algorithm.

A new approach for evaluating node importance in complex networks via deep learning methods

The evaluation of node importance is a critical research topic in network science, widely applied in social networks, transport systems, and computer networks. Prior works addressing this topic either consider a single metric or assign weights for multiple metrics or select features by handcraft, which exist one-sidedness and subjectivity issues. In this paper, to tackle these problems, we propose a new approach named CGNN to identify influential nodes based on deep learning methods, including Convolutional Neural Networks (CNNs) and Graph Neural Networks (GNNs). CGNN obtains the feature matrices by the contraction algorithm and gets the labels by the Susceptible-Infected-Recovered (SIR) model, which will be leveraged for learning the hidden representations of nodes without utilizing any network metrics as features. We adopt three evaluation criteria to verify CGNN concerning effectiveness and distinguishability, including Kendall’s τ correlation coefficient, monotonicity index (MI), and ranking distribution function (RDF). Nine baselines are employed to compare with CGNN on thirty synthetic networks and twelve real-world networks from different domains. Simulation results demonstrate that CGNN manifests better performance than the baselines, in which the values of τ are large and significantly increase, the values of MI approach to 1, and the points in the RDF curves distribute more uniformly. These results may provide reference significance for controlling epidemic spreading and enhancing network robustness.

Identifying Important Nodes in Complex Networks Based on Node Propagation Entropy.

In recent years, the identification of the essential nodes in complex networks has attracted significant attention because of their theoretical and practical significance in many applications, such as preventing and controlling epidemic diseases and discovering essential proteins. Several importance measures have been proposed from diverse perspectives to identify crucial nodes more accurately. In this paper, we propose a novel importance metric called node propagation entropy, which uses a combination of the clustering coefficients of nodes and the influence of the first- and second-order neighbor numbers on node importance to identify essential nodes from an entropy perspective while considering the local and global information of the network. Furthermore, the susceptible–infected–removed and susceptible–infected–removed–susceptible epidemic models along with the Kendall coefficient are used to reveal the relevant correlations among the various importance measures. The results of experiments conducted on several real networks from different domains show that the proposed metric is more accurate and stable in identifying significant nodes than many existing techniques, including degree centrality, betweenness centrality, closeness centrality, eigenvector centrality, and H-index.

DDMF: A Method for Mining Relatively Important Nodes Based on Distance Distribution and Multi-Index Fusion

In research on complex networks, mining relatively important nodes is a challenging and practical work. However, little research has been done on mining relatively important nodes in complex networks, and the existing relatively important node mining algorithms cannot take into account the indicators of both precision and applicability. Aiming at the scarcity of relatively important node mining algorithms and the limitations of existing algorithms, this paper proposes a relatively important node mining method based on distance distribution and multi-index fusion (DDMF). First, the distance distribution of each node is generated according to the shortest path between nodes in the network; then, the cosine similarity, Euclidean distance and relative entropy are fused, and the entropy weight method is used to calculate the weights of different indexes; Finally, by calculating the relative importance score of nodes in the network, the relatively important nodes are mined. Through verification and analysis on real network datasets in different fields, the results show that the DDMF method outperforms other relatively important node mining algorithms in precision, recall, and AUC value.

Node importance ranking method in complex network based on gravity method

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. Now, 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 object, 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 used to represente 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 locally and highly clustering characteristics as core nodes when performing <i>k</i>-core decomposition, which leads to the inaccuracy of the gravity algorithm. Based on the universal gravitation method, considering the node <i>H</i> 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<sub>+</sub>. The SIR model is used to simulate the propagation process in 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.

Identifying Critical Nodes Based on Feature Engineering

To mine important nodes in complex networks is very important for analyzing and governing real complex systems. Designing a good indicator that reflects the importance of nodes is a key issue on efficiently and accurately mining critical nodes. On the bases of the neighbor information of nodes, the features that can effectively reflect the local structure of nodes are extracted through feature extraction and reconstruction. The relational model between local structure and real importance of nodes is established by utilizing regression model based on the extracted features. The experimental results on 13 real networks show that the proposed method outperforms the benchmark methods of critical nodes identification.

A new model to identify node importance in complex networks based on DEMATEL method

It is still a hot research topic to identify node importance in complex networks. Recently many methods have been proposed to deal with this problem. However, most of the methods only focus on local or path information, they do not combine local and global information well. In this paper, a new model to identify node importance based on Decision-making Trial and Evaluation Laboratory (DEMATEL) is presented. DEMATEL method is based on graph theory which takes the global information into full consideration so that it can effectively identify the importance of one element in the whole complex system. Some experiments based on susceptible-infected (SI) model are used to compare the new model with other methods. The applications in three different networks illustrate the effectiveness of the new model.

Method for measuring node importance in complex networks based on local characteristics

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.

Identifying influential links to control spreading of epidemics

In recent years, epidemics have been raging around the world, causing serious harm to human health, and controlling the spread of the epidemics has become a hot topic. The study of network partition is of great practical significance to control the spread of the epidemics. Network partition is an NP hard problem. Much work has focused on identifying important nodes in complex networks to achieve network partition. Similarly, understanding the importance of links in spreading dynamics in a network can provide ways to hinder or slow down ongoing dynamical phenomena like the spreading of epidemic or the diffusion of information. This paper studies the algorithms to identify influential links in complex networks. Deleting some influential links can divide the network into some components so as to prevent effectively the spreading processes in epidemics. Our algorithms can successfully identify influential links at low computational cost by utilizing the eigenvector centrality measures. The simulated results in some real-world social networks and synthetic networks show that our algorithms are effective. The number of infected individuals can be remarkable reduced by removing influential links.

An improved gravity model to identify influential nodes in complex networks based on k-shell method

To find the important nodes in complex networks is a fundamental issue. A number of methods have been recently proposed to address this problem but most previous studies have the limitations, and few of them considering both local and global information of the network. The location of node, which is a significant property of a node in the network, is seldom considered in identifying the importance of nodes before. To address this issue, we propose an improved gravity centrality measure on the basis of the k-shell algorithm named KSGC to identify influential nodes in the complex networks. Our method takes the location of nodes into consideration, which is more reasonable compared to original gravity centrality measure. Several experiments on real-world networks are conducted to show that our method can effectively evaluate the importance of nodes in complex networks.

Local volume dimension: A novel approach for important nodes identification in complex networks

How to identify important nodes in complex networks? It is still an open problem. Many methods have been proposed to tackle this problem. The main contribution of this paper is to propose a method to identify important nodes based on local volume dimension (LVD). If the LVD of the node is lower, the node is more important. Promising results of experiments on four real-world networks compared with six methods under both Susceptible–Infected (SI) model and Susceptible–Infected–Recovered (SIR) model validate and demonstrate the effectiveness of the proposed method.