Problem In Complex Networks Research Articles

Delay-induced consensus of fractional-order complex networks via intermittent sampled position control

This paper investigates the consensus problem of fractional-order complex networks via intermittent sampled position control. A delay-induced consensus protocol with intermittent sampled position for the fractional-order system is proposed, where only the current and delayed sampled positions are used. Meanwhile, the controllers operate only for a period of time in each sampling interval, which decrease the working time and update rates of controllers. Successively, by discussing four situations involving delay, sampling period, and communication width, necessary and sufficient consensus criteria are presented. It is interesting to find the delay has a positive impact on consensus of fractional-order complex networks, since consensus cannot be achieved without delay under the proposed protocol. Finally, simulation examples are presented to illustrate the theoretical analysis.

A controllability method on the social Internet of Things (SIoT) network

In recent years, one type of complex network called the Social Internet of Things (SIoT) has attracted the attention of researchers. Controllability is one of the important problems in complex networks and it has essential applications in social, biological, and technical networks. Applying this problem can also play an important role in the control of social smart cities, but it has not yet been defined as a specific problem on SIoT, and no solution has been provided for it. This paper addresses the controllability problem of the temporal SIoT network. In this regard, first, a definition for the temporal SIoT network is provided. Then, the unique relationships of this network are defined and modeled formally. In the following, the Controllability problem is applied to the temporal SIoT network (CSIoT) to identify the Minimum Driver nodes Set (MDS). Then proposed CSIoT is compared with the state-of-the-art methods for performance analysis. In the obtained results, the heterogeneity (different types, brands, and models) has been investigated. Also, 69.80 % of the SIoT sub-graphs nodes have been identified as critical driver nodes in 152 different sets. The proposed controllability deals with network control in a distributed manner.

Event-triggered impulsive control for nonlinear stochastic delayed systems and complex networks

In this paper, we probe the pth moment exponential stability (p−ES) of stochastic delayed systems subject to event-triggered delayed impulsive control (ETDIC), where the impulsive intensities are assumed to be positive random variables. Based on event-triggered mechanism (ETM) in the sense of expectation, some new sufficient conditions are developed to ensure the stability of the addressed system with Zeno-free behavior. The Lyapunov–Razumikhin method is adopted to handle the time-varying delay in continuous dynamics, and the concept of average random impulsive estimation (ARIE) is introduced to reduce the design requirements of the controller. Especially, the proposed ETDIC strategy not only generates the impulse time sequence according to the predesigned ETM, but also removes the limitations on the size of time delays. Furthermore, the ETM serves as a solution for synchronization problems in complex neural networks. Finally, two examples are given to illustrate the effectiveness of our conclusions.

Event-Based Distributed Set-Membership Estimation for Complex Networks Under Deception Attacks

This paper addresses the problem of event-based distributed set-membership estimation for complex networks with unknown but bounded (UBB) disturbances. To reflect the compromised data transmissions in cyber security, deception attacks are taken into consideration. Meanwhile, a novel estimation model is proposed against UBB disturbances. In order to schedule the signal transmissions between nodes and remote estimators, a novel decentralized dynamic periodic event-triggered mechanism (DPETM) with a time-varying threshold is developed for each node of the complex networks, which reduces the waste of communication resources and the complexity of computation. Thereafter, a series of distributed set-membership estimators are designed, whose parameters are explicitly determined in terms of the resolution of a particular linear matrix inequality (LMI) related to the information of the communication topology. An optimized ellipsoid estimation set is obtained by applying a recursive optimization algorithm. Finally, the simulation results are shown to demonstrate the viability of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by set-membership state estimation problem of complex networks in practical missions, such as military, environment, industry, etc. The set-membership estimation of complex networks provides a reliable confidence region for each system node. Event-triggered control is an effective method for the design of set-membership estimator. But the common results require the systems to monitor the measurements point-to-point, which leads to the huge consumption of calculation and communication resources. For this reason, this paper originally extends the DPETM to the discrete-time version from the field of continuous-time systems. Meanwhile, this paper considers the deception attacks in communication channels, and the generic framework established earlier can tackle simultaneously sector-bounded nonlinearity, UBB disturbances, and deception attacks. The main difficulty of this paper lies in the analysis for the sawtooth constraint of periodic samplings. For this difficulty, we introduce a piecewise auxiliary function, which is similar with the loop-function in the field of continuous-time systems. Together with recursive optimization algorithm, the detailed analysis method is proposed for the reliable confidence regions of each set-membership estimator.

Closeness and Vertex Residual Closeness of Harary Graphs

Analysis of a network in terms of vulnerability is one of the most significant problems. Graph theory serves as a valuable tool for solving complex network problems, and there exist numerous graph-theoretic parameters to analyze the system’s stability. Among these parameters, the closeness parameter stands out as one of the most commonly used vulnerability metrics. Its definition has evolved to enhance the ease of formulation and applicability to disconnected structures. Furthermore, based on the closeness parameter, vertex residual closeness, which is a newer and more sensitive parameter compared to other existing parameters, has been introduced as a new graph vulnerability index by Dangalchev. In this study, the outcomes of the closeness and vertex residual closeness parameters in Harary Graphs have been examined. Harary Graphs are well-known constructs that are distinguished by having n vertices that are k-connected with the least possible number of edges.

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.

Mixed-integer linear programming formulations and column generation algorithms for the Minimum Normalized Cuts problem on networks

This paper deals with the k-way normalized cut problem in complex networks. It presents a methodology that uses mathematical optimization to provide mixed-integer linear programming formulations for the problem. The paper also develops a branch-and-price algorithm for the above-mentioned problem which scales better than the compact formulations. Additionally, a heuristic algorithm which is able to approximate large-scale image problems in those cases where the exact methods are not applicable is presented. Extensive computational experiments assess the usefulness of these methods to solve the k-way normalized cut problem. Finally, we have applied the minimum normalized cut objective function to the segmentation of actual images, showing the applicability of the introduced methodology.

A Comprehensive Review of Similarity Based Link Prediction Methods for Complex Networks including Computational Biology

Information retrieval is one of the most challenging tasks for the mankind and to retrieve information interaction is required, which ultimately leads to the formation of networks. Universe is packed with different type of networks. Networks with complex topological properties are called complex network. Such types of networks are major tools for learning the connection between the organizations and finding the purpose of complex systems. The link prediction problems in complex networks facilitate predictions about the future organization of the network. Network is represented as a graph. The data in the network is signified by nodes, and the relations are represented by links. The future of non-connected links amid node pairs is predicted. This paper reviews the methods used to predict links for complex networks using similarity-based heuristics. Previous reviews, despite having a clear outline of the link prediction study, only described the prediction approaches. Research gaps between the similarity-based link prediction techniques, however, were not explicitly stated. With the help of chronological findings and a research gaps approach, this review seeks to give a continuing review and introduce the link prediction.

GNR: A universal and efficient node ranking model for various tasks based on graph neural networks

Node ranking is an essential problem in complex networks, which aims to identify influential or central nodes in a graph. Existing methods for node ranking are either computationally expensive or suboptimal for different networks and multiple tasks. In this paper, we propose GNR, a graph neural network-based node ranking model that can sort nodes quickly and efficiently for any type of networks. To achieve this, GNR takes into account three factors to calculate the importance of nodes and train the model: degree, infection score, and dismantling score, which capture the local and global structure of the network and the effect of nodes on network propagation and dismantling. We conduct extensive experiments on 16 real networks, and compare GNR with other centrality-based node ranking models on three tasks: network dismantling, virus propagation, and information spreading. The results show that GNR performs better in most cases and validates the effectiveness and superiority of our model.

Application of linear ordinary differential equations to the stability control of long time lag networks

Abstract Optimal control based on the exact synchronization of linear ordinary differential equations can provide conditions for the existence of optimal control of long-time lag network stability. In this paper, we first generalize network control systems, time lag systems, and modern control system stability theory to discuss long-time lag network stability analysis and control problems. The numerical solution method for solving ordinary differential equations with boundary conditions is proposed by combining the numerical solution method for initial value problems of differential equations and the iterative method for solving nonlinear equations. Finally, the fixed-time synchronization problem of complex networks with time-varying time lags under periodic intermittent control is studied. Two intermittent control strategies are designed based on the linear ordinary differential equation algorithm, and the convergence analysis of the synchronization error and the synchronization criterion are given. Numerical values show that the synchronization error converges to zero (&lt; 1.0e − 5) in 0.32s, while the convergence times are 0.55s and 0.90s. The fixed times of the three methods are calculated to be T * = 0.52, T 1 = 0.71 and T 2 = 1.32, respectively, and the synchronization error system converges faster under the method in the paper. The numerical simulation results verify the effectiveness of linear ordinary differential equations in controlling the stability of long-time lag networks.

Adaptive Exponential Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay.

In recent years, the adaptive exponential synchronization (AES) problem of delayed complex networks has been extensively studied. Existing results rely heavily on assuming the differentiability of the time-varying delay, which is not easy to verify in reality. Dealing with nondifferentiable delay in the field of AES is still a challenging problem. In this brief, the AES problem of complex networks with general time-varying delay is addressed, especially when the delay is nondifferentiable. A delay differential inequality is proposed to deal with the exponential stability of delayed nonlinear systems, which is more general than the widely used Halanay inequality. Next, the boundedness of the adaptive control gain is theoretically proved, which is neglected in much of the literature. Then, the AES criteria for networks with general delay are established for the first time by using the proposed inequality and the boundedness of the control gain. Finally, an example is given to demonstrate the effectiveness of the theoretical results.

Synchronization of multi-weighted complex networks with mixed variable delays and uncertainties via impulsive pinning control

In this paper, the synchronization problem in nonlinearly-coupled multi-weighted complex networks with parameter uncertainties and multiple delays, where both internal time-varying delays and multiple coupling time-varying delays are included, is investigated by adopting a pinning impulsive control scheme, which combines the merits of pinning control and impulsive control. Impulsive pinning control ratio has been applied to select controlled nodes at each impulsive instant. Based on the Lyapunov function method, sufficient conditions for achieving complete synchronization of multi-weighted complex networks have been derived. And numerical simulations are presented to demonstrate the validity and efficacy of our derived theoretical results, which show that under the criteria proposed in this paper, multi-weighted complex networks with parameter uncertainties and multiple delays, could achieve complete synchronization by applying pinning impulsive control. Besides, taking bus lines as the network nodes, a public traffic roads network model with multi-weights is established and analyzed numerically as an application of the proposed multi-weighted complex network model.

General optimization framework for accurate and efficient reconstruction of symmetric complex networks from dynamical data.

The challenging problem of network reconstruction from dynamical data can in general be formulated as an optimization task of solving multiple linear equations. Existing approaches are of the two types: Point-by-point (PBP) and global methods. The local PBP method is computationally efficient, but the accuracies of its solutions are somehow low, while a global method has the opposite traits: High accuracy and high computational cost. Taking advantage of the network symmetry, we develop a novel framework integrating the advantages of both the PBP and global methods while avoiding their shortcomings: i.e., high reconstruction accuracy is guaranteed, but the computational cost is orders of magnitude lower than that of the global methods in the literature. The mathematical principle underlying our framework is block coordinate descent (BCD) for solving optimization problems, where the various blocks are determined by the network symmetry. The reconstruction framework is validated by numerical examples with a variety of network structures (i.e., sparse and dense networks) and dynamical processes. Our success is a demonstration that the general principle of exploiting symmetry can be extended to tackling the challenging inverse problem or reverse engineering of complex networks. Since solving a large number of linear equationsis key to a plethora of problems in science and engineering, our BCD-based network reconstruction framework will find broader applications.

Fixed-Time Synchronization of Multilayer Complex Networks Under Denial-of-Service Attacks

This paper addresses the fixed-time synchronization (FXTS) problem of multilayer complex networks (MCNs) under denial-of-service (DoS) attacks. Generally, when a control strategy is introduced, it will be affected by DoS attacks. Considering the DoS attacks that occur in the control channel, the model of MCNs under DoS attacks is constructed. Using the average non-attack rate of intermittent attacks and the Lyapunov method, the fixed-time convergence theorem is given to achieve the FXTS of the MCNs. The results indicate that the settling time has a connection with the controller parameters and the attack parameters. Moreover, we find that the higher the average non-attack rate of the intermittent attacks, the shorter the settling time of FXTS. Besides, the energy consumption of the control strategy is estimated. Finally, the feasibility of the theoretical results is verified by Chua’s circuit in numerical simulations.

Density-Based Entropy Centrality for Community Detection in Complex Networks.

One of the most important problems in complex networks is the location of nodes that are essential or play a main role in the network. Nodes with main local roles are the centers of real communities. Communities are sets of nodes of complex networks and are densely connected internally. Choosing the right nodes as seeds of the communities is crucial in determining real communities. We propose a new centrality measure named density-based entropy centrality for the local identification of the most important nodes. It measures the entropy of the sum of the sizes of the maximal cliques to which each node and its neighbor nodes belong. The proposed centrality is a local measure for explaining the local influence of each node, which provides an efficient way to locally identify the most important nodes and for community detection because communities are local structures. It can be computed independently for individual vertices, for large networks, and for not well-specified networks. The use of the proposed density-based entropy centrality for community seed selection and community detection outperforms other centrality measures.

Dismantling networks abruptly by tree decomposition

Dismantling a network by removing the minimum vertices is a challenging problem in complex networks. While most existing methods focus on efficiency, they overlook the importance of abruptness during the dismantling process. Gradual changes in the largest connected component size can alert the target and render the attack ineffective. To overcome this issue, we propose a new dismantling method based on tree decomposition and a new metric quantifying the abruptness of the dismantling process. Our method involves applying tree decomposition to the network using the min fill-in method, identifying the most critical edge in the decomposed tree, and removing the vertices contained in the edge. Experimental results on eight real networks demonstrate that our proposed method significantly outperforms classical methods in abruptness and efficiency.

Synchronization of Delayed Complex Networks on Time Scales via Aperiodically Intermittent Control Using Matrix-Based Convex Combination Method.

This article reconsiders synchronization problem of linear complex networks with time-varying delay on time scales. For different types of time scales, aperiodically intermittent control scheme is established by using a matrix-based convex combination method, which has great potential in reducing control consumption and saving communication bandwidth. By employing a common Lyapunov function, aperiodically intermittent controllers are utilized successfully to achieve synchronization of linear delayed complex networks on special time scales onto an isolated node. Next, by constructing a special Lyapunov function with time-varying coefficients, sufficient criteria that consist of two linear matrix inequalities are demonstrated to make linear delayed complex networks on general time scales synchronized onto an isolated system with an exponential convergence rate given in advance. Due to delayed complex networks in this article defined on time scales, the proposed control schemes are applicable to continuous-time networks, their discrete-time forms, and any combination of them. Four numerical examples are offered to highlight the effectiveness and superiority of the proposed aperiodically intermittent control schemes at last.

Adaptive finite-time pinned and regulation synchronization of disturbed complex networks

This paper investigates robust adaptive pinning control strategies and coupling regulation algorithms to deal with the finite-time synchronization problem of nonlinear complex networks in the presence of general disturbances. First, the concept of finite-time synchronized stability is employed in the sense of finite-time stability. To eliminate the negative impacts of disturbances and nonlinear dynamics, adaptive technique is developed so that the state-dependent rate and constant bounds of disturbances and nonlinear dynamics can be suitably estimated on line. Then, combining the adaptive estimations and Lyapunov functions, pinning control strategies for pinned nodes and two kinds of coupling regulation algorithms for un-pinned nodes are developed to achieve the finite-time bounded synchronization results of the complex dynamical network. Finally, simulation results are carried out to demonstrate the proposed control and regulation methods and their effectiveness.

Finite-time synchronization of complex networks with partial communication channels failure

This paper addresses the finite-time synchronization problem of complex networks under a new communication constraint. The situation that some communication channels used to transmit sub-information between two nodes may fail is considered, which causes the receiving node to be unable to obtain complete state information. Moreover, due to less information transmission between nodes, the analysis of finite-time synchronization problem becomes more difficult. Therefore, several questions naturally arise here: Under this communication restriction, how to remodel the complex network, and can the network achieve finite-time synchronization? To better solve these questions, the complex network model with partial communication channels failure is established first. Then, based on the finite-time stability theory and state layered method, two finite-time synchronization criteria for complex networks are provided. Finally, the effectiveness of obtained results are verified by numerical simulations.

Deep Learning with Graph Convolutional Networks: An Overview and Latest Applications in Computational Intelligence

Convolutional neural networks (CNNs) have received widespread attention due to their powerful modeling capabilities and have been successfully applied in natural language processing, image recognition, and other fields. On the other hand, traditional CNN can only deal with Euclidean spatial data. In contrast, many real-life scenarios, such as transportation networks, social networks, reference networks, and so on, exist in graph data. The creation of graph convolution operators and graph pooling is at the heart of migrating CNN to graph data analysis and processing. With the advancement of the Internet and technology, graph convolution network (GCN), as an innovative technology in artificial intelligence (AI), has received more and more attention. GCN has been widely used in different fields such as image processing, intelligent recommender system, knowledge-based graph, and other areas due to their excellent characteristics in processing non-European spatial data. At the same time, communication networks have also embraced AI technology in recent years, and AI serves as the brain of the future network and realizes the comprehensive intelligence of the future grid. Many complex communication network problems can be abstracted as graph-based optimization problems and solved by GCN, thus overcoming the limitations of traditional methods. This survey briefly describes the definition of graph-based machine learning, introduces different types of graph networks, summarizes the application of GCN in various research fields, analyzes the research status, and gives the future research direction.