Evaluation Method Of Node Importance Research Articles

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.

The node importance evaluation method based on graph convolution in multilayer heterogeneous networks

ABSTRACT Node importance evaluation is a hot issue in complex network analysis. Existing node importance evaluation methods are mainly oriented to homogeneous networks, which ignore the heterogeneity of node types and edges. We propose an MLN critical node evaluation method based on graph convolution. In this paper, we generate the feature matrix of nodes. Considering the diversity of node types in the network, we design an adapted node sampling method based on the meta path. An MLN node embedding model is constructed based on a graph convolutional network (MGC). Besides, the negative sampling technique is used to complete MGC training. Metrics of critical node evaluation are constructed by combining the node embedding vectors and local structural features to evaluate the node's importance. The experimental results show that the proposed method has better evaluation accuracy than the K-Shell algorithm (K-Shell), K-shell-based gravity model ranking algorithm (KSDG), the Page Rank algorithm in MLN (PR), influence maximization based on network embedding (IMNE) and the node ranking algorithm based on information entropy (ERM).

Hybrid weighted communication network node importance evaluation method

Communication networks are used as an important guarantee for information interaction and efficient collaboration within many fields and systems; however, under information technology conditions, the destruction of a number of nodes in a network may have a great impact on the overall operation of the network. Therefore, it is important to accurately determine the critical nodes in the network to enhance the network’s resistance to destruction. Combining the characteristic attributes of the communication network, a node contribution evaluation matrix is proposed based on the efficiency matrix, from the perspective of node receiving information; a node value evaluation matrix is proposed from the perspective of a node providing information to neighboring nodes, and node importance is calculated by integrating the evaluation results of the two matrices and the node’s own attributes. The algorithm is suitable for directed-weighted network node value evaluation, and the effectiveness and accuracy of the algorithm are verified by comparing other algorithms for a small-scale network. In further experimental validation, a hybrid weighted communication network evolution model based on organizational structured networks is proposed, and networks of different sizes are generated for experimental simulation. The results show that when nodes with high importance are removed from the network, they can cause a rapid decrease in the network efficiency and maximum connectivity, confirming the accuracy of the algorithm in evaluating the importance of nodes and identifying critical nodes in the network.

Correlation Study of Temporal Climate Networks Based on Weighted Cumulative Node Evaluation

In order to systematically analyze the characteristics of climate change in China in recent years, this paper selects the data of 6 climate factors from China meteorological stations during 1984-2016 for 33 years. With the help of complex network theory, the representative climate nodes in China are determined by node importance evaluation method with the power to accumulate intermediate centrality. Multiple single-factor temporal static and temporal dynamic climate network models are constructed to explore the correlation of representative node networks of Climate in China. The results show that the temperature network has the strongest correlation. The temporal static network has the weakest correlation with precipitation network, while the temporal dynamic network has the weakest correlation with wind velocity network and shows a weak fluctuation downward trend.

Node Importance Evaluation Method of Satellite Information Network Based on Heterogeneous Virtual Subnet

The node importance evaluation method is of great significance for studying the robustness and routing strategies of satellite information network. According to the heterogeneous characteristics of nodes in satellite information network, they can be abstracted into two types of virtual connected nodes, and then the satellite information network model based on multi-virtual subnet is constructed. Furthermore, the node importance evaluation method based on heterogeneous virtual subnet (named HVS_based NIE) is proposed through the defined parameters such as normalization degree of virtual nodes, virtual node betweenness and correlation factor, which can accurately evaluate the node importance of satellite information network. Results of case analysis show that compared with classical graph theory algorithm, the proposed HVS_based NIE algorithm not only considers the network connectivity, but also considers the impact of data throughput on the nodes importance of satellite network, so as to evaluate the nodes importance of satellite network more accurately.

Evaluation Method for Node Importance of Urban Rail Network Considering Traffic Characteristics

As a sustainable means of public transport, the safety of the urban rail transit is a significant section of public safety and is highly important in urban sustainable development. Research on the importance of urban rail stations plays an important role in improving the reliability of urban rail networks. This paper proposed an improved method for evaluating the importance of urban rail stations in a topology network, which was used to identify the key stations that affect the urban rail network performance. This method was based on complex network theory, considering the traffic characteristics of the urban rail network that runs on specific lines and integrating the structural characteristics and interrelationship of the lines where the stations are located. Hereafter, this method will be abbreviated as CLI. In order to verify that the high importance stations evaluated by this method were the key stations that had a great impact on the urban rail network performance, this paper designed a comparative attack experiment of betweenness centrality and CLI. The experiment was carried out by taking the Suzhou Rail Transit (SZRT) network as an example and the largest connected subgraph as well as the network efficiency as indicators to measure the network performance. The results showed that CLI had a greater impact on network performance and could better evaluate the key stations in the urban rail network than node degree and betweenness centrality.

NIE-GAT: node importance evaluation method for inter-domain routing network based on graph attention network

Evaluating node importance in inter-domain routing networks to protect key nodes is crucial to the stability of the Internet. Existing evaluation methods struggle to balance accuracy and speed: centrality-based methods are quick but lack accuracy, while impact-based methods are precise but have high computational complexity. Approaches in the complex network field do not consider the business relationships in the inter-domain routing network, so their results may not match reality. This paper proposes a novel method for node importance evaluation in the inter-domain routing networks, called NIE-GAT. The key idea of NIE-GAT is to map a node’s static features to its dynamic cascading failure impact by a deep learning model based on the graph attention network. Additionally, several node centrality features based on the business relationships are defined. A method for calculating node impact labels with the cascading failure model is also designed. The experimental results on real inter-domain routing networks of different scales show that the evaluation accuracy of NIE-GAT for the top 3% nodes reaches more than 93%, which is over 7% higher than the existing best method. For large-scale networks with more than ten thousand nodes, NIE-GAT can complete the evaluation within 2 min.

Traffic Node Importance Evaluation Based on Clustering in Represented Transportation Networks

With the ability to acquire and process large-scale traffic big data, a cooperative intelligent transport system can be realized. Identifying important nodes in a traffic network contributes to better traffic control, which plays a more critical role in improving the traffic efficiency of a cooperative intelligent transport system. However, existing traffic node importance evaluation methods rely on manually designed metrics such as betweenness, degree, which may lead to biased results. Meanwhile, the traditional method of iteratively deleting nodes is unsuitable for a large-scale traffic network. In this paper, we propose a novel traffic node importance evaluation method based on clustering in represented transportation network. Specifically, the proposed method first construct a length-weighted network based on the geographic road network. Then, it learns the low-dimensional embeddings of nodes employing network representation learning. Finally, it clusters each nodes with a machine learning method and identifies the critical nodes through vehicle flow of different nodes. Experimental results on the real-word dataset show that our proposed method has excellent performance compared to baseline methods.

Overlapping Community Detection Based on Node Importance and Adjacency Information

Detecting the community structure and predicting the change of community structure is an important research topic in social network research. Focusing on the importance of nodes and the importance of their neighbors and the adjacency information, this article proposes a new evaluation method of node importance. The proposed overlapping community detection algorithm (ILE) uses the random walk to select the initial community and adopts the adaptive function to expand the community. It finally optimizes the community to obtain the overlapping community. For the overlapping communities, this article analyzes the evolution of networks at different times according to the stability and differences of social networks. Seven common community evolution events are obtained. The experimental results show that our algorithm is feasible and capable of discovering overlapping communities in complex social network efficiently.

Identifying Influential SLD Authoritative Name Servers on the Internet

DNS plays an important role on the Internet. The addressing of most applications depends on the proper operation of DNS. The root servers and the top-level domain servers are relied upon by many domains on the Internet, and their security affects the whole Internet. As a result, more attention has been paid to the security of servers at these two levels. However, the security of second-level domains and their servers also needs to be brought to the forefront. This paper focuses on showing the complex resolving dependencies and identifying influential name servers for second-level domains. We start by detecting domain name resolution paths and building up a name dependency graph. Then we construct domain name resolution networks of different numbers and sizes, which are connected by a certain number of domain name resolution graphs. On this basis, the network is analyzed from the perspective of complex network analysis, and a multi-indicators node importance evaluation method based on partial order is proposed to identify the influential name servers of the network. Once these name servers are not properly configured and fail or are compromised by DDoS attacks, it will cause resolution failure for a wide range of domain names.

Evaluation method of node importance in temporal satellite networks based on time slot correlation

Temporal satellite networks can accurately describe the dynamic process of satellite networks by considering the interaction relationship and interaction sequence between satellite nodes. In addition, the measurement of node importance in satellite networks plays a crucial role in understanding the structure and function of the network. The classical supra-adjacency matrix (SAM) temporal model identifies the key nodes in the temporal network to some extent, which ignores the differences of inter-layer connectivity relationships leading to the inability to reflect the dynamic variations of satellite nodes. Therefore, the evaluation method based on time slot correlation is proposed to measure the importance of satellite nodes in this paper. Firstly, the correlation coefficient of time slot nodes is defined to measure the coupling relationship of adjacent time slots. Secondly, the dynamic supra-adjacency matrix (DSAM) temporal network model is proposed considering the correlation between adjacent time slots and the characteristics of link time. Finally, the node importance ranking results in each time slot and a global perspective are obtained by utilizing the eigenvector centrality. Experimental simulations of the Iridium and Orbcomm constellations demonstrate that the DSAM method has a relatively accurate recognition rate and high stability.

Robustness evaluation of the air cargo network considering node importance and attack cost

With the rapid development of e-commerce and express industry, the air cargo network has become an important infrastructure. How to ensure the network robustness is of great importance for its operational safety. However, few robustness researches considered the attack cost. Furthermore, the traditional degree indexes are disabled to represent the node importance comprehensively. To solve these problems, considering the topological structure, industry characteristics, and the directionality of the air cargo network simultaneously, we propose a novel node importance evaluation method based on the TOPSIS method to better measure the attack cost. Then, an optimal attack strategy model considering attack cost constraints is proposed to achieve better effects. In order to verify the effectiveness of the proposed method, a real case study of China's air cargo network in 2017 is carried out. The results show that the proposed node importance index can better represent the node importance than the traditional degree indexes. Besides, the optimal attack strategy will change according to different attack budgets and the importance which defenders attach to the critical nodes, and the proposed optimal attack strategy model can achieve a higher attack effect than other strategies.

Research on Importance Evaluation of Complex Product Parts Based on Multilayer Complex Network

The identification and evaluation of important parts play an important role in effective production arrangement and shortening the product development in the product design stage. In this paper, a complex product node importance evaluation method based on multilayer network is proposed to identify and evaluate importance parts faster. First, a complex product design expression network based on “function behavior structure (FBS)” multilayer complex network is established. Second, the evaluation index system of important design parts for complex products based on multilayer network is constructed. Third, a three-parameter grey relational model based on the fuzzy analytic hierarchy process and the Gini coefficient method is proposed. Finally, this method is available and feasible through taking the large permanent magnet synchronous centrifugal unit as an example.

Comprehensive Evaluation Method for Network Node Importance based on Constructed Tree

The importance measurement of nodes in directed weighted networks is of great significance for theoretical research and practical application of networks. Aiming at the directed weighted network model in actual networks, based on the special transformation of graphs and tree roots, this paper proposes a comprehensive quantitative assessment method for the importance index of nodes based on the directed weighted network’s global properties, local attributes, network location and bidirectionally propagation. This method transforms the nodes to be analyzed in the graph to root, constructs a bidirectional depth-affected XD tree and a breadth-affected XB tree with the node to be evaluated as the root of the tree. Then comprehensively consider the two-way influence of the node level, node neighbors and the closeness between neighbors in the two trees constructed, and the in-out effects, build a deep impact evaluation model at the two-way level, two-way neighbor information and comprehensive evaluation index of clustering coefficient. By calculating the comprehensive importance value of each node in the network, the comprehensive ranking of the importance of the nodes in the network can finally be obtained. The robustness experiment of ARPA network shows that the G value of the important node quantified by this method has absolute advantages, this method can effectively analyze key nodes in the network.

An Entropy-Based Self-Adaptive Node Importance Evaluation Method for Complex Networks

Identifying important nodes in complex networks is essential in disease transmission control, network attack protection, and valuable information detection. Many evaluation indicators, such as degree centrality, betweenness centrality, and closeness centrality, have been proposed to identify important nodes. Some researchers assign different weight to different indicator and combine them together to obtain the final evaluation results. However, the weight is usually subjectively assigned based on the researcher’s experience, which may lead to inaccurate results. In this paper, we propose an entropy-based self-adaptive node importance evaluation method to evaluate node importance objectively. Firstly, based on complex network theory, we select four indicators to reflect different characteristics of the network structure. Secondly, we calculate the weights of different indicators based on information entropy theory. Finally, based on aforesaid steps, the node importance is obtained by weighted average method. The experimental results show that our method performs better than the existing methods.

Importance Evaluation of C4ISR Communication Nodes Based on Multi-attribute Decision-making

Node importance is a key measuring index for network structure characteristics. Evaluating the nodes importance can locate key nodes of the network and provide support for network node planning. The importance of the C4ISR communication node reflects the dependence degree of the functional nodes and functional links on the C4ISR transport nodes. How to transform this qualitative dependence into quantitative dependency measuring is the core problem of evaluating node importance and locating key nodes. Based on the quantitative dependence measuring, this paper proposes a C4ISR communication node importance evaluation method based on multi-attribute decision-making. Meanwhile, the applicability of the method is verified by examples.

Node importance evaluation method based on multi-attribute decision-making model in wireless sensor networks

Identifying important nodes is very crucial to design efficient communication networks or contain the spreading of information such as diseases and rumors. The problem is formulated as follows: given a network, which nodes are the more important? Most current studies did not incorporate the structure change as well as application features of a network. Aiming at the node importance evaluation in wireless sensor networks, a new method which ranks nodes according to their structural importance and performance impact is proposed. Namely, this method considers two aspects of the network, network structural characteristics and application requirements. This method integrates four indicators which reflect the node importance, namely, node degree, number of spanning trees, delay, and network energy consumption. Firstly, the changes in the four indicators are analyzed using the node deletion method. Then, the TOPSIS multi-attribute decision-making method is applied to merge these four evaluation indicators. On this basis, a more comprehensive evaluation method (MADME) for node importance is obtained. Theory study reveals MADME method saves computational time. And the simulation results show the superiority of the MADME method over various algorithms such as the N-Burt method, betweenness method, DEL-Node method, and IE-Matrix method. The accuracy of the evaluation can be improved, and the key nodes determined by the MADME method have a more obvious effect on the network performance. Our method can provide guidance on influential node identification in the network.

Evaluation method for node importance based on attraction between nodes

Vital node, which has some special functions, plays an important role compared to other nodes in complex networks. Recently, the discovery of vital nodes in complex networks has captured increasing attention due to their important theoretical significance and great practicability. By defining the confidence of the node and the inter-node attraction, the significance of the node is measured by the product of the confidence of the node and the aggregation of attractions of the node on other nodes in the network. The experimental results illustrate that the proposed method has higher precision and performs well on various networks with different structures.

A New Evaluation Method of Node Importance in Directed Weighted Complex Networks

AbstractCurrent researches on node importance evaluation mainly focus on undirected and unweighted networks, which fail to reflect the real world in a comprehensive and objective way. Based on directed weighted complex network models, the paper introduces the concept of in-weight intensity of nodes and thereby presents a new method to identify key nodes by using an importance evaluation matrix. The method not only considers the direction and weight of edges, but also takes into account the position importance of nodes and the importance contributions of adjacent nodes. Finally, the paper applies the algorithm to a microblog-forwarding network composed of 34 users, then compares the evaluation results with traditional methods. The experiment shows that the method proposed can effectively evaluate the node importance in directed weighted networks.

Evaluation method of node importance in directed-weighted complex network based on multiple influence matrix

In complex networks, the node importance evaluation is of great significance for studying the robustness of network. The existing methods of evaluating the node importance mainly focus on undirected and unweighted networks, which fail to reflect the real scenarios comprehensively and objectively. In this paper, according to the directed and weighted complex network model, by analyzing the local importance of the nodes and the dependencies among all the nodes in the whole network, a new method of evaluating the node importance based on a multiple influence matrix is proposed. Firstly, the method defines the concept of cross strength to characterize the local importance of the nodes. The index not only distinguishes between the in-strength and out-strength of the nodes, but also helps to discriminate the differences in importance among each with an in-degree of 0. In addition, to characterize the global importance of the nodes to be evaluated, we use the total important influence value of all the nodes exerted on the nodes, which makes up the deficiencies of the other evaluation methods which just depend on adjacent nodes. Emphatically, in the analysis of the influence ratio of source node on node to be evaluated, we not only take into account the distance factor between nodes, but also introduce the number of the shortest path factors. In order to make the evaluation algorithm more accurate, according to the number of the shortest paths, we present two perspectives to analyze how other factors affect the influence ratio. One is to evaluate how this source node exerts important influence on the other nodes to be evaluated. The other is to analyze how the other source nodes perform important influence on this node to be evaluated. In view of the above factors, three influence matrices are constructed, including the efficiency matrix, and the other two influence matrices from the perspectives of fixing source nodes and target nodes, respectively. Then, we use analytic hierarchy process to weight the three matrices, thereby obtaining the multiple influence matrix, which makes the global importance evaluation more comprehensive. Finally, the method is applied to typical directed weighted networks. It is found that compared with other methods, our method can effectively distinguish between nodes. Furthermore, we carry out simulation experiments of cascading failure on each method. The simulation results further verify the effectiveness of the proposed method.