Problem In Complex Networks Research Articles

Partial Pinning Control for the Synchronization of Fractional-Order Directed Complex Networks

This paper mainly studies the synchronization problem of fractional-order directed complex networks through partial pinning control. Unlike other papers, the network studied in this paper is neither strongly connected nor contains directed spanning trees. By utilizing the directed acyclic graph condensation and Layering theory, the network is decomposed into several strong connected components and then divided into layers. It proved that all or part of nodes in the network can achieve synchronization with the pinner’s trajectory, only when the root strong connected components in the upstream of these nodes are pinned and satisfy some sufficient conditions. In addition, according to the ControlRank algorithm, an optimized strategy is designed to solve the problem of the optimal selection of the pinning nodes to ensure the specific nodes of the network can achieve synchronization eventually. Meanwhile the amount of control energy cost will also be given in this paper. Finally, two simulation examples are given to verify the reliability and feasibility of the optimized algorithm.

Event-triggered sampled-data synchronization of complex networks with time-varying coupling delays

This paper investigates the event-triggered sampled-data synchronization problem of complex networks with time-varying coupling delays. The sampled-data controller is designed with event-triggered mechanisms. Some results in terms of a linear matrix inequality are obtained to guarantee the asymptotical synchronization of complex networks with time-varying coupling delays. Lastly, we test the effectiveness of the proposed method via some numerical examples.

Complex network routing strategy based on segmented transportation distance limit

In transmission problem of many complex networks, there are some restrictions on the routing path between a pair of sources and destinations, especially for the transmission process that has a segment distance limit, which has a wide range of applications in real transportation, information transmission, etc. on large real networks. In this work, we constructed a complex network transmission model, defined the transmission distance limit to [Formula: see text] and randomly selected a part of the nodes in the scale-free network as the station. Based on the shortest path algorithm and a weighted routing algorithm, we observed the results under the transmission distance limit. The results show that the setting of [Formula: see text] is important, which can be used to guide and control the fuel carrying capacity of vehicles on the transportation network. Finally, we selected two real road network for simulation and the results demonstrate the effectiveness of the algorithm in scale-free networks and real networks.

Compact models for influential nodes identification problem in directed networks

Influential nodes identification problem (INIP) is one of the most important problems in complex networks. Existing methods mainly deal with this problem in undirected networks, while few studies focus on it in directed networks. Moreover, the methods designed for identifying influential nodes in undirected networks do not work for directed networks. Therefore, in this paper, we investigate INIP in directed networks. We first propose a novel metric to assess the influence effect of nodes in directed networks. Then, we formulate a compact model for INIP and prove it to be NP-Complete. Furthermore, we design a novel heuristic algorithm for the proposed model by integrating a 2-opt local search into a greedy framework. The experimental results show that, in most cases, the proposed methods outperform traditional measure-based heuristic methods in terms of accuracy and discrimination.

Identifying critical nodes in complex networks via graph convolutional networks

Critical nodes of complex networks play a crucial role in effective information spreading. There are many methods have been proposed to identify critical nodes in complex networks, ranging from centralities of nodes to diffusion-based processes. Most of them try to find what kind of structure will make the node more influential. In this paper, inspired by the concept of graph convolutional networks(GCNs), we convert the critical node identification problem in complex networks into a regression problem. Considering adjacency matrices of networks and convolutional neural networks(CNNs), a simply yet effectively method named RCNN is presented to identify critical nodes with the best spreading ability. In this approach, we can generate feature matrix for each node and use a convolutional neural network to train and predict the influence of nodes. Experimental results on nine synthetic and fifteen real networks show that under Susceptible–Infected–Recovered (SIR) model, RCNN outperforms the traditional benchmark methods on identifying critical nodes under spreading dynamic.

A Community Discovery Algorithm for Complex Networks

Community structure is an important feature of complex networks. These community structures have the fractal characteristics, that is, there is a self similarity of statistical sense between the complex networks and their local. There have been more and more recent researches on communities’ discovery in complex network. However, most existing approaches require the complete information of entire network, which is impractical for some networks, e.g. the dynamical network and the network that is too large to get the whole information. Therefore, the study of community discovery in complex networks has rather important theoretical and practical value. Through the analysis and study of the complex network evolution models with renormalization and the community change of the complex network evolution, using the tool of adjusting scales as the renormalization process, a multi-scale network community detection algorithm based on fractal feature evolution was proposed. The purpose is to solve community discovery problems in dynamic complex networks, and the effectiveness of the proposed method is verified by real data sets. By comparing result of this paper with the previous methods on some real world networks, and experimental results verify the feasibility and accuracy.

A systematic mapping study for blockchain based on complex network

SummaryBlockchain has started to appear as a potentially reliable and underlying technology for various fields. There have been lots of surveys focusing on blockchain with respect to specific topics, such as security, architecture, applications, and so on. However, a systematic mapping study, including all related fields about blockchain, has been largely ignored. In this article, we revisit the problem of complex networks in the form of scientific collaboration networks. More specifically, we utilize the method of systematic mapping and implement them into blockchain technology. We collect 233 articles by searching Baidu scholar with the keyword “blockchain,” then construct two complex networks according to the relationship of keywords and authors, respectively. The keywords' complex network is a small‐world network while the authors' complex network is not. Furthermore, the tool of Netdraw provides a visualized graph for the complex network. Meanwhile, we find some subgroups in the network, which may highlight the future direction of blockchain.

Pinning synchronization control of complex networks with partial couplings

In this article, the pinning synchronization problem of complex networks with a target node via sampled-data communications is considered. Due to partial couplings among the nodes in complex networks, a decoupling method is adopted to investigate each channel of complex networks independently. By constructing a time-dependent Lyapunov function, it is proved that the pinning synchronization of complex networks with a target node can be achieved if the control parameters are appropriately selected. Furthermore, further study is needed to investigate the pinning synchronization of complex networks in the presence of constant delay. A novel criterion is obtained using Jensen’s inequality and Wirtinger’s inequality. It is worth noting that the lower and upper bounds of the sampling intervals can be calculated by linear matrix inequality box of MATLAB. Theoretical results are well verified through a numerical simulation.

Structural Controllability for a Class of Complex Networks With Root Strongly Connected Components

Structural controllability of complex networks has been an attractive research area, and Minimum Inputs Theorem was proposed to identify the minimum driver nodes for complex networks with one-dimensional node dynamics. Then, the Minimum Inputs Theorem was extended to the complex network with multidimensional node dynamics by looking the multidimensional node as a subnetwork. However, when the structures of these subnetworks possess the root Strongly Connected Components that have perfect matching, the minimum driver nodes of these subnetworks are not sufficient to guarantee the full control, and some extra nodes are needed to be controlled. Therefore, in this paper, we study the structural controllability of complex networks with multidimensional node dynamics whose corresponding subnetworks possess such root Strongly Connected Components. First, we apply the Maximum Matching principle to the network topology to obtain which subnetworks we need to control. Then, an algorithm is proposed to identify a feasible minimum controlled node set of the subnetwork. Finally, by analyzing the structural features of the whole network and synthetically applying the proposed algorithm, Maximum Matching principle and Graphical Approach, a flowchart is given for identifying the minimum controlled node set of the whole network. By duality, the above results can also apply to the structural observability problem of such complex networks.

Synchronization of stochastic multi-weighted complex networks with Lévy noise based on graph theory

This paper addresses the synchronization problem of stochastic multi-weighted complex networks with Lévy noise. Based on the drive-response concept and graph theory, global Lyapunov function of the error network between drive-response networks is obtained by the weighted summation of Lyapunov functions of vertex systems. According to the stochastic analysis and state feedback control technique, the rigorous synchronization analysis of drive-response networks in the pth moment and probability sense is presented. The obtained synchronization criteria are closely related with multi-weights and the intensity of Lévy noise. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.

An integral sliding mode approach to distributed control of coupled networks with measurement Quantization

This paper is concerned with the distributed sliding mode control problem of complex networks under quantization mechanism. The complex networked control system is considered with inner coupling, uncertainties and quantized measurements among the agents. The quantizer, which is adopted as a logarithmic one, is designed to be on the sensor unit to implement the digital communication. In order to avoid the discontinuity of the sliding mode control law, namely, the sliding surface, an adaptive filter is utilized. Based on the filtered signal, an integral sliding-mode manifold is designed for each agent. A series of dynamic sliding mode control laws are synthesized to achieve the exponential reaching onto the sliding surface within a finite time for the whole networked system. The resulting sliding motion is analyzed using the Lyapunov functional approach, and a finite-gain L2 stability criterion is established. Finally, the effectiveness of the designed distributed sliding mode control scheme is illustrated with some simulation results.

Centralized/decentralized event-triggered pinning synchronization of stochastic coupled networks with noise and incomplete transitional rate

This paper studies the synchronous problem of Markovian switching complex networks associated with partly unknown transitional rates, stochastic noise, and randomly coupling strength. In order to achieve the synchronization for these array networks, event-triggered pinning control is established and developed, in which the pinning node undergoes a self-adapted switch, governed by a Markov chain. Two types of event-triggered sampling controls, centralized and decentralized event-triggered sampling, respectively, are established. Sufficient conditions for synchronization are developed by constructing a desirable stochastic Lyapunov functional as well as by employing the properties of Markov chain and Itoˆ integration. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach.

On Almost Controllability of Dynamical Complex Networks with Noises

This paper discusses the controllability problem of complex networks. It is shown that almost any weighted complex network with noise on the strength of communication links is controllable in the sense of Kalman controllability. The concept of almost controllability is elaborated by both theoretical discussions and experimental verifications.

Pinning event‐triggered control for stochastic discrete‐time complex networks with time‐varying delay

In this study, the distributed event-triggered control strategy is found to cope with the pinning control problem of stochastic discrete-time complex networks with time-varying delay. Under the devised mechanism, exponential mean-square synchronisation can be implemented in the directed networks. By utilising the Lyapunov functional method and the stochastic analysis, several sufficient conditions are established. Moreover, the issue of average synchronisation is investigated. For the stochastic complex networks without reference state, it is demonstrated that all nodes can converge to a time-varying weighted average exponentially by a suitable distributed event-triggered controller. Finally, some numerical examples are presented to indicate the effectiveness of the devised control strategies.

Multi-moth flame optimization for solving the link prediction problem in complex networks

Providing a solution for the link prediction problem attracts several computer science fields and becomes a popular challenge in researches. This challenge is presented by introducing several approaches keen to provide the most precise prediction quality within a short period of time. The difficulty of the link prediction problem comes from the sparse nature of most complex networks such as social networks. This paper presents a parallel metaheuristic framework which is based on moth-flame optimization (MFO), clustering and pre-processed datasets to solve the link prediction problem. This framework is implemented and tested on a high-performance computing cluster and carried out on large and complex networks from different fields such as social, citation, biological, and information and publication networks. This framework is called Parallel MFO for Link Prediction (PMFO-LP). PMFO-LP is composed of data preprocessing stage and prediction stage. Dataset division with stratified sampling, feature extraction, data under-sampling, and feature selection are performed in the data preprocessing stage. In the prediction stage, the MFO based on clustering is used as the prediction optimizer. The PMFO-LP provides a solution to the link prediction problem with more accurate prediction results within a reasonable amount of time. Experimental results show that PMFO-LP algorithm outperforms other well-regarded algorithms in terms of error rate, the area under curve and speedup. Note that the source code of the PMFO-LP algorithm is available at https://github.com/RehamBarham/PMFO_MPI.cpp .

Containment control of directed networks with time-varying nonlinear multi-agents using minimum number of leaders

In this paper, the problem of containment control with minimum number of leaders in arbitrary directed networks consisting of time-varying nonlinear multi-agents is investigated. Unlike the existing containment control problem with redundant leaders in special networks, we consider the problem with minimum number of leaders in arbitrary directed networks. We show that the problem of finding the minimum number of leaders can be converted into a minimum spanning tree problem by introducing a toll station connecting with each agent. By employing the developed Edmonds’ algorithm, the minimum number of leaders is located at the roots of each tree in the obtained spanning forest. This situation allows us to achieve containment control in a distributed manner. On the basis of this situation, a distributed protocol is developed to address the containment control of multi-agent systems with time-varying nonlinear dynamics. Simulation results are provided to illustrate the efficiency of the proposed methodology. Our work makes it possible for studying and extending application of containment control problems in various complex networks.

Solving the speed and accuracy of box-covering problem in complex networks

The box-covering method that covers a network with a minimum number of boxes is critical to demonstrate network fractals and the re-normalization analysis of complex networks. Moreover, one is able to investigate the network structure by analyzing the re-normalization flow or categorizing networks into several universal classes. A number of compelling methods are not well adapted to the large-scale networks due to high time complexity, or low accuracy. In this paper, we introduce a hybrid method that has high accuracy and low time consumption based the maximum-excluded-mass-burning (MEMB) method and the random sequential (RS) method. Our method combines the characteristics of the MEMB method that search as fewer boxes as possible with the high efficiency of the RS method by selecting a few unimportant central nodes, especially for large-scale networks. We also optimize the storage mechanism of the method so that the excluded mass of nodes can be updated efficiently. Experiments in the real networks with different structures demonstrate that the improvement of our method can be substantial. Our method reduces the time consumption of the MEMB method by more than 40% with only 10% more boxes than the MEMB method.

Exponential synchronization of stochastic complex networks with multi-weights: A graph-theoretic approach

This paper concerns the exponential synchronization problem of stochastic complex networks with multiple weights (SCNMW). By the method of network split, SCNMW can be modelled as stochastic coupled systems driven by Brownian motion. By combining graph theory, Lyapunov stability theory and state feedback control technique, drive-response synchronization criteria of SCNMW have been obtained. Two kinds of exponential synchronization criteria are obtained, one is given with Lyapunov functions of vertex systems, and the other is shown with the coefficients of SCNMW. The obtained synchronization principles are closely related to the coupling strength of multiple sub-networks and the intensity of noise perturbation. Finally, a numerical example with some simulations is presented to illustrate the theoretical results.

Solving Management Problems in Water Distribution Networks: A Survey of Approaches and Mathematical Models

Modern water distribution networks (WDNs) are complex and difficult to manage due to increased level of urbanization, varying consumer demands, ageing infrastructure, operational costs, and inadequate water resources. The management problems in such complex networks may be classified into short-term, medium-term, and long-term, depending on the duration at which the problems are solved or considered. To address the management problems associated with WDNs, mathematical models facilitate analysis and improvement of the performance of water infrastructure at minimum operational cost, and have been used by researchers, water utility managers, and operators. This paper presents a detailed review of the management problems and essential mathematical models that are used to address these problems at various phases of WDNs. In addition, it also discusses the main approaches to address these management problems to meet customer demands at the required pressure in terms of adequate water quantity and quality. Key challenges that are associated with the management of WDNs are discussed. Also, new directions for future research studies are suggested to enable water utility managers and researchers to improve the performance of water distribution networks.

Maximizing Network Resilience against Malicious Attacks

The threat of a malicious attack is one of the major security problems in complex networks. Resilience is the system-level self-adjusting ability of a complex network to retain its basic functionality and recover rapidly from major disruptions. Despite numerous heuristic enhancement methods, there is a research gap in maximizing network resilience: current heuristic methods are designed to immunize vital nodes or modify a network to a specific onion-like structure and cannot maximize resilience theoretically via network structure. Here we map complex networks onto a physical elastic system to introduce indices of network resilience, and propose a unified theoretical framework and general approach, which can address the optimal problem of network resilience by slightly modifying network structures (i.e., by adding a set of structural edges). We demonstrate the high efficiency of this approach on three realistic networks as well as two artificial random networks. Case studies show that the proposed approach can maximize the resilience of complex networks while maintaining their topological functionality. This approach helps to unveil hitherto hidden functions of some inconspicuous components, which in turn, can be used to guide the design of resilient systems, offer an effective and efficient approach for mitigating malicious attacks, and furnish self-healing to reconstruct failed infrastructure systems.