Nodes In Complex Networks Research Articles

Fast Identification of Critical Nodes in Complex Network Based on Improved Greedy Algorithm

Abstract Over the past decades, many critical and complex systems, such as power grid, transportation network, and information network, have been effectively modeled using complex network. However, these networks are susceptible to cascading failure, triggered by minor failure, leading to partial or total collapse. Preventing cascading failure necessitates the protection of critical nodes within the network, making the identification of these nodes particularly crucial. In this paper, we introduce an Improved Greedy Algorithm (IGA), inspired by the traditional greedy algorithm and the relationship between the propagation mechanism of cascading failure and N-K failure. This algorithm gets rid of the shortcomings of traditional recognition algorithms for dealing with large-scale networks with long time and low accuracy, and evaluates the critical degree of nodes based on network connectivity and overload rate. The simulation is carried out in Barabsi-Albert (BA) network and IEEE 39-, 118-bus systems, and make comparisons with other different algorithms. The results show that IGA not only has low computational complexity, but also has high accuracy in identifying critical nodes in complex networks.

Identifying Key Nodes for the Influence Spread Using a Machine Learning Approach

The identification of key nodes in complex networks is an important topic in many network science areas. It is vital to a variety of real-world applications, including viral marketing, epidemic spreading and influence maximization. In recent years, machine learning algorithms have proven to outperform the conventional, centrality-based methods in accuracy and consistency, but this approach still requires further refinement. What information about the influencers can be extracted from the network? How can we precisely obtain the labels required for training? Can these models generalize well? In this paper, we answer these questions by presenting an enhanced machine learning-based framework for the influence spread problem. We focus on identifying key nodes for the Independent Cascade model, which is a popular reference method. Our main contribution is an improved process of obtaining the labels required for training by introducing “Smart Bins” and proving their advantage over known methods. Next, we show that our methodology allows ML models to not only predict the influence of a given node, but to also determine other characteristics of the spreading process—which is another novelty to the relevant literature. Finally, we extensively test our framework and its ability to generalize beyond complex networks of different types and sizes, gaining important insight into the properties of these methods.

Higher-order structure based node importance evaluation in directed networks

Evaluating the significance of objects with possible relevant information is a crucial topic in information science. Due to the fact that objects related to each other can often be described using complex networks, this topic also forms a fundamental theme in network science. Most traditional methods for characterizing the importance of nodes in complex networks only utilize the binary relationships between node pairs, neglecting the influence brought by higher-order structures. Considering the specific interaction modes between local nodes in the network, this paper associates the higher-order structural characteristics of the network with the importance of the nodes. It constructs an evaluation framework for the importance of nodes in directed networks based on higher-order structures. Experimental analysis on both artificial data and scientific citation data from the APS dataset has validated the effectiveness of the proposed algorithms. Compared with PageRank and eigenvector centrality, the proposed algorithms demonstrated higher accuracy, revealing the role of higher-order structures in node importance evaluation. Finally, a robustness analysis of several algorithms indicated that the proposed algorithms exhibited good robustness.

Identifying influential nodes in complex networks through the k-shell index and neighborhood information

Identifying influential nodes in complex networks through the k-shell index and neighborhood information

Isolating Centrality-Based Generalization of Traditional Centralities to Discover Vital Nodes in Complex Networks

Isolating Centrality-Based Generalization of Traditional Centralities to Discover Vital Nodes in Complex Networks

Optimization method for protecting the robustness of first-order nodes in complex networks

Optimization method for protecting the robustness of first-order nodes in complex networks

Identification of important nodes in multi-layer hypergraphs based on fuzzy gravity model and node centrality distribution characteristics

Hyperedge is a common structure that represents high-order interactions between nodes in complex networks, and multi-layer networks provide more diverse node interactions than single-layer networks. Therefore, multi-layer hypergraphs can more clearly represent the relationships between nodes. However, there are few studies on identifying important nodes in this framework. This paper proposes a method called HCT to fill this gap. It consists of three parts, namely: Hypergraph Fuzzy Gravity Model (HFGM), Layer Weight Calculation Method based on Node Centrality Distribution Characteristics (CDLW) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). HCT progressively analyzes the importance of a node from three levels: local (the node itself), semi-local (the hyperedges and community to which the node belongs), and global (the layer to which the node belongs). By combining these three results, the global centrality of a node in the entire network can be calculated. Simulation experiments demonstrate that the important nodes identified by HCT exhibit stronger contagion capabilities in nine networks compared to nine combinatorial methods and removing these nodes will seriously damage the connectivity and robustness of the network. The centrality of each node calculated by HCT is also consistent with its actual importance.

Response to the comment on “Identifying critical nodes in complex networks based on distance Laplacian energy”

The following is a point-by-point response to Wang and Sun's comment on “Identifying critical nodes in complex networks based on distance Laplacian energy”.

A graph convolutional network model based on regular equivalence for identifying influential nodes in complex networks

The identification of influential nodes in complex networks is an interesting problem. Traditional approaches, such as metric- and machine learning-based approaches, often fail to adequately consider the network structure or node features, limiting their applications in certain scenarios. Deep learning-based methods, particularly those using graph neural networks (GNNs), have yielded remarkable results in this field. However, there is a lack of utilization of the regular equivalence-based similarity between nodes to feature construction, which is critical to deep learning-based methods. Nevertheless, regular equivalence-based similarity is extremely suitable to the quantification of the similarity between influential nodes, as these nodes usually have similar structural properties but do not require common neighbors. Building upon graph convolutional network (GCN, a specific type of GNN) and the regular equivalence-based similarity, this study proposes a novel method for identifying influential nodes in complex networks. Particularly, the regular equivalence-based similarities between nodes are considered to construct node features; a GCN is enhanced to improve the identification of influential nodes. Experiments on several datasets indicate that the proposed method is superior to state-of-the-art methods, demonstrating the advantages of the proposed feature construction based on regular equivalence-based similarity over the identification of influential nodes.

A Key Node Mining Method Based on K-Shell and Neighborhood Information

Mining key nodes in complex networks has always been a promising research direction in the field of complex networks. Many precise methods proposed by researchers for mining influential special nodes in networks have been widely applied in a plethora of fields. However, some important node-mining methods often use the degree as a node attribute indicator for evaluating node importance, while the clustering coefficient, as an important attribute of nodes, is rarely utilized. Some methods only consider the global position of nodes in the network while ignoring the local structural information of nodes in special positions and the network. Hence, this paper introduces a novel node centrality method, KCH. The KCH method leverages K-shell to identify the global position of nodes and assists in evaluating the importance of nodes by combining information such as structural holes and local clustering coefficients of first-order neighborhoods. This integrated approach yields an enhanced performance compared to existing methods. We conducted experiments on connectivity, monotonicity, and zero models on 10 networks to evaluate the performance of KCH. The experiments revealed that when compared to the collective influence baseline methods, such as social capital and hierarchical K-shell, the KCH method exhibited superior capabilities in terms of collective influence.

Identifying influential nodes: A new method based on dynamic propagation probability model

Identifying influential nodes in complex networks persists as a crucial issue due to its practical applications in the real world. The propagation model is a special method for identifying influential nodes based on propagation dynamics. However, most of propagation-based methods have not delved deeply into the impact of network topology on the propagation process. In this paper, we propose a method based on the dynamic propagation probability model, called DPP. The main idea of this method is to characterize the impact of a node on the basis of its propagation capacity during propagation process by using dynamic propagation probability within its three level neighborhood. This new metric redefines the propagation probability of neighbors by refining the propagation process, which allows the propagation probability to be transmitted in accordance with the network structure. To validate the performance of the proposed method, we compare with eight different methods from four aspects in 11 real-world networks. The experimental results demonstrate that the DPP method has good performance in most cases.

Finding influential nodes in complex networks based on Kullback–Leibler model within the neighborhood

As a research hot topic in the field of network security, the implementation of machine learning, such as federated learning, involves information interactions among a large number of distributed network devices. If we regard these distributed network devices and connection relationships as a complex network, we can identify the influential nodes to find the crucial points for optimizing the imbalance of the reliability of devices in federated learning system. This paper will analyze the advantages and disadvantages of existing algorithms for identifying influential nodes in complex networks, and propose a method from the perspective of information dissemination for finding influential nodes based on Kullback–Leibler divergence model within the neighborhood (KLN). Firstly, the KLN algorithm removes a node to simulate the scenario of node failure in the information dissemination process. Secondly, KLN evaluates the loss of information entropy within the neighborhood after node removal by establishing the KL divergence model. Finally, it assesses the damage influence of the removed node by integrating the network attributes and KL divergence model, thus achieving the evaluation of node importance. To validate the performance of KLN, this paper conducts an analysis and comparison of its results with those of 11 other algorithms on 10 networks, using SIR model as a reference. Additionally, a case study was undertaken on a real epidemic propagation network, leading to the proposal of management and control strategies for daily protection based on the influential nodes. The experimental results indicate that KLN effectively evaluates the importance of the removed node using KL model within the neighborhood, and demonstrate better accuracy and applicability across networks of different scales.

State estimation and structure identification of complex networks with time‐varying delays and model uncertainty based on probabilistic graph neural network

SummaryIn this paper, the state estimation problem and structure identification problem are investigated for an array of complex networks with time‐varying delays and model uncertainty. Model uncertainty is generated by uncertain connections between nodes in complex networks. Combining probabilistic graph model and graph neural network, a probabilistic graph neural network is proposed to deal with the uncertainty, and the multiple linear terms of the errors between nodes are estimated. The purpose of the addressed state estimation problem is to design a state estimator such that, in the presence of the model uncertainty, the estimation error to converge to zero can be guaranteed and the explicit expression of the estimator parameters is given. Based on a Lyapunov function, the parameters of the estimator and the updating laws of the weights of probabilistic graph neural network can be obtained by the solutions to linear matrix inequalities. The purpose of the addressed structure identification problem is to infer a definite graph structure model based on Bayes' theorem in the presence of a stable probabilistic graph neural network and state estimator. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation and structure identification scheme.

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.

A new semi-local centrality for identifying influential nodes based on local average shortest path with extended neighborhood

Quantifying the importance of nodes in complex networks is known as the problem of identifying influential nodes and is considered a critical aspect in interacting with these networks. This problem has many applications such as controlling rumors, sickness spreading, and viral marketing, where its importance has been understood by the research society in the last decade. This paper proposes a new semi-local centrality to identify influential nodes in complex networks based on the theory of Local Average Shortest Path with extended Neighborhood concept (LASPN). LASPN focuses on a distributed technique to extract the subgraph associated with each node and apply the average shortest path theory to it. We use the extended neighborhood concept to find the nearest neighbors of each node with low complexity, where this can lead to high efficiency in dealing with large-scale networks. In addition to applying relative changes in the average shortest path, the proposed metric considers the importance of the node itself as well as its nearest neighbors in ranking the nodes. Evaluation of the proposed centrality metric has been done through numerical simulations on several real-world networks. The results based on Kendall's τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au$$\\end{document} coefficient under the SIR infection spreading model show that LASPN improves the performance by 2.7% compared to the best available equivalent method.

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.

Identifying Influential Nodes in Complex Networks From Semi-Local and Global Perspective

Identifying Influential Nodes in Complex Networks From Semi-Local and Global Perspective

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.

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.