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  15 February 2026, Volume 23 Issue 1 Previous Issue   
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Complex Network
Study of Grid Cascading Faults Based on Second-order Neighbor Load Redistribution Strategy   Collect
HU Jinmei, ZOU Yanli, WANG Hongjun, ZHANG Hai
Complex Systems and Complexity Science. 2026, 23 (1): 1-9.   DOI: 10.13306/j.1672-3813.2026.01.001
Abstract ( 133 )     PDF (4782KB) ( 27 )  
In this paper, we study the enhancement of network robustness by changing the range of load redistribution in grid cascading faults, and propose a load redistribution strategy considering second-order neighbors. Single-node attack and multi-node attack experiments are conducted on the western United States power grid and Polish power grid using this strategy to analyze the robustness of the network under different load redistribution strategies and different attack methods. Simulation experiments show that the redistribution strategy proposed in this paper shows better robustness and destruction resistance on multiple networks. In addition, a comparative study with the load redistribution strategy that considers higher-order neighbors reveals that there is a saturation effect in the redistribution strategy of the load, and the strategy proposed in this paper is the optimal choice to balance the distribution efficiency and the network robustness.
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Weighted Directed Network Evaluation Algorithm Based on Propagation Model   Collect
ZHANG Xiruo, LIAO Yuan, PENG Jiaqin, YANG Yuhang, HUANG Liya
Complex Systems and Complexity Science. 2026, 23 (1): 10-16.   DOI: 10.13306/j.1672-3813.2026.01.002
Abstract ( 124 )     PDF (2368KB) ( 15 )  
To investigate node importance in the extensive weighted directed networks in real-world scenarios, this paper proposes the Cross K-Propagation Number (CKPN) algorithm, which is a node evaluation algorithm for weighted directed networks based on propagation models. This algorithm analyzes node information from both local and global perspectives, examines the interaction between nodes under different propagation orders and adjusts the contribution allocation of the in-degree and out-degree in the directed network. ARPA network, WSIR model and deliberate attack model are used to verify the effectiveness of the proposed method. The results show that the CKPN algorithm considers the information comprehensively and the evaluation results are detailed. It has good effect in large-scale networks and is more accurate than the traditional algorithm that only considers the network topology.
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Evolutionary Mechanism of Green Technology Innovation Network in the Yellow River Basin   Collect
XIANG Bowen, XU Ying, XU Gaofeng
Complex Systems and Complexity Science. 2026, 23 (1): 17-25.   DOI: 10.13306/j.1672-3813.2026.01.003
Abstract ( 112 )     PDF (3266KB) ( 18 )  
To study the evolutionary mechanism of green technology innovation network in the Yellow River Basin, this study, using social network analysis and the index random graph model, analyzed the evolution characteristics and mechanisms of green technology innovation networks in the Yellow River Basin from 2011 to 2019. The findings are as follows: The scale and cooperation intensity of the innovation network continuously increased, with small-world and scale-free properties remaining significant, but connection closeness decreased. In the upstream Yellow River Basin, it transitioned from a single-core innovation cluster centered around Xi'an in Phase One (2011-2013) to three innovation clusters: Qinghai, Ning-Shaan-Yu, and Gan-Inner Mongolia-Jin in Phase Two (2017-2019). In the downstream region, single-core clusters around Jinan and Qingdao in Phase One integrated into the Shandong Peninsula Urban Agglomeration innovation cluster in Phase Two. Organizational and cultural proximity facilitate intercity innovation but also amplify provincial and cultural "boundary effects." City clusters and basin proximity did not create "boundary effects," but policy and basin proximity did not promote intercity cooperation. Geographic and technological proximity, city scale, innovation levels, and green innovation levels positively impact intercity innovation. This study's "proximity-boundary" analysis framework contributes to understanding innovation network impact mechanisms and provides theoretical and policy support for optimizing the green innovation system in the basin.
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Identification of Key Stations and Routes in Urban Metro and Conventional Bus Networks from a Resilience Perspective   Collect
SUN Xiaohui, LIU Yi, MI Yumei, LÜ Kai
Complex Systems and Complexity Science. 2026, 23 (1): 26-36.   DOI: 10.13306/j.1672-3813.2026.01.004
Abstract ( 136 )     PDF (3874KB) ( 47 )  
Urban Metro and conventional bus carry a significant portion of residents' daily travel services, and their disruption due to sudden incidents often results in widespread and profound impacts. To ensure safe and efficient operation of public transportation, based on complex network theory, a method is proposed from the perspective of structural resilience for identifying key stations and routes of urban metro and conventional bus networks through importance, that is the resilience-based mean square deviation-TOPSIS comprehensive evaluation method. The reliability of this method is respectively verified through the monotonicity of the importance evaluation results, the robustness analysis of different attack strategies, and the comparative analysis of construction timelines. The case study results show that this method can well differentiate each station in the network; when conducting robustness analysis, it can also reflect the characteristic that key stations with greater importance have a larger impact on the overall network performance; the K-means clustering results of the importance of Shenzhen metro lines are generally consistent with the construction timeline. The reliability of this method in identifying key stations and routes is verified comprehensively.
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Electricity Theft Detection Based on Multiscale Residual Attention Network   Collect
CHANG Hanyun, CHEN Lishen, QIAN Jianghai
Complex Systems and Complexity Science. 2026, 23 (1): 37-44.   DOI: 10.13306/j.1672-3813.2026.01.005
Abstract ( 115 )     PDF (2517KB) ( 11 )  
Aiming at the shortcomings of traditional power theft detection methods, which only use one-dimensional power, rely on manual features, and have low detection accuracy, an eletricity theft detection model based on multiscale residual attention network is proposed. The model is based on pyramidal convolution to fully extract multi-scale detail features, and introduces hybrid dilated convolutional attention residual network to improve the detection performance. In this paper, the proposed method is experimentally validated using the public dataset of the State Grid, and the results show that compared with the traditional logistic regression, support vector machine, random forest, and other models, the AUC, MAP, and F1 score indexes of the proposed model have achieved effective improvement.
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Causation Analysis for Hazardous Materials Transportation Accident Based on Meta-network Model   Collect
REN Cuiping, ZHANG Jiaqian
Complex Systems and Complexity Science. 2026, 23 (1): 45-52.   DOI: 10.13306/j.1672-3813.2026.01.006
Abstract ( 117 )     PDF (1695KB) ( 14 )  
In order to reveal the key factors of hazardous materials transportation accidents and the structural relationship between factors, a new node system is established with agent, behavior, consequence, organization, environment and event as elements, using the meta-network model, combined with the characteristics of hazardous materials road transportation. Taking the major transportation explosion accident of ‘6.13’liquefied petroleum gas tank truck in Wenling, Zhejiang Province as an example, constructed the meta-network of hazardous materials transportation accidents and analyzed the structural characteristics and strike strategies of the network. It is found that the network of hazardous materials transportation accidents presents the characteristics of sparse network. The key strike effect with the closeness centrality is the best.
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Routability Prediction for FPGA Design Based on Complex Networks and Attention Mechanism   Collect
NIE Tingyuan, WANG Yanwei, NIE Jingjing, LIU Pengfei
Complex Systems and Complexity Science. 2026, 23 (1): 53-59.   DOI: 10.13306/j.1672-3813.2026.01.007
Abstract ( 117 )     PDF (1626KB) ( 12 )  
FPGA routability prediction is of great significance for solving the optimization of physical design. We propose an FPGA routability prediction model based on complex networks and CBAM-CNN. During the placement phase, we extract circuit features and complex network features related to circuit congestion and map them to RGB images. We introduce an attention mechanism to enhance the importance of features. The experimental results show that the prediction accuracy is 98.03%, precision is 98.3%, sensitivity is 98.3%, specificity is 97.67%, and the Matthews correlation coefficient is 93.75%. The importance of complex network features in FPGA routability prediction is ranked in order of degree, strength, eigenvector, and betweenness. This proves the effectiveness and importance of complex network features in predicting FPGA routability.
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Robustness Analysis of the World Airline Network Considering Multiple Variables   Collect
HU Zuoan, YANG Jianghao, DENG Jincheng
Complex Systems and Complexity Science. 2026, 23 (1): 60-69.   DOI: 10.13306/j.1672-3813.2026.01.008
Abstract ( 107 )     PDF (4057KB) ( 23 )  
Due to the inadequacy of using a single indicator to evaluate the air network robustness, it is necessary to further consider multiple indicators and their core variables to propose a comprehensive evaluation method, in order to analyze and evaluate the network robustness comprehensively, this paper considered multiple variables such as the number of remaining nodes, the number of neighbor links, and the shortest path, to establish a comprehensive robustness evaluation index. Set up four failure scenarios and simulated them on the four networks. The simulation results show that, under random failure, the World-Airline Network has the highest robustness among the four networks, and its comprehensive robustness index only drops to zero after almost all nodes fail; under three malicious failure scenarios, the World-Airline Network fails to maintain robustness when a small number of nodes fail, and collapses completely when about 20% of nodes fail; under three malicious failure strategies, the comprehensive robustness curves of the World-Airline Network are basically consistent, which proves the universality of this comprehensive robustness metric.
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Robustness Optimization Strategy for Networks Based on Peripheral Nodes of Communities   Collect
PAN Wenxiang, LI Dongyan, SUN Sixiang, TONG Ning
Complex Systems and Complexity Science. 2026, 23 (1): 70-78.   DOI: 10.13306/j.1672-3813.2026.01.009
Abstract ( 103 )     PDF (3238KB) ( 14 )  
To improve the efficiency of the network robustness optimization strategy, the impacts of several major types of optimization strategies on the structure of urban infrastructure networks were analyzed. A strategy called Community Periphery nodes link Addition (CPA) was proposed to optimize network robustness. This strategy uses the Girvan-Newman algorithm to determine the community structure of complex networks, regards each community as a network, uses the K-shell algorithm to determine the position of the network center within each community, identifies the node within each community which is least affected by the network center as the community periphery node, and establishes edges based on these periphery nodes. The experimental results based on the real infrastructure network and BA scale-free network model demonstrate that compared with classical strategies,such as random edge addition strategy, low-degree addition strategy, low-betweenness addition strategy, and algebraic connectivity addition strategy, the CPA strategy generally achieves higher efficiency in improving network robustness.
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A Convergence Iterative Method for the Evolution of Complex Networks Based on Adjacency Matrices   Collect
MOU Qifeng, LI Xiaoqian
Complex Systems and Complexity Science. 2026, 23 (1): 79-86.   DOI: 10.13306/j.1672-3813.2026.01.010
Abstract ( 121 )     PDF (2777KB) ( 20 )  
To efficiently address the continuous splitting and recombination of complex network topological structures and reduce computational resource consumption, a method called adjacency matrix fusion iteration is proposed. The complex network aggregation is achieved through the fusion of adjacency matrix row-column vectors, the steps and forms of network evolution fusion and splitting iteration are defined, and empirical analysis is carried out as an example of constructing a flight guarantee network. Finally, the fusion splitting process of the directed network is simulated, and time and space complexity indicators are introduced to verify the effectiveness of the method. The results show that the proposed method is consistent with the evolutionary generation process of the empirical network topology, and its arithmetic complexity is lower than that of other methods, which is especially suitable for the study of directed dense networks.
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Identification of Important Nodes in Complex Networks Based on    Node Influence Factor and Contribution Factor   Collect
SUN Wenjing, YU Lufen, PAN Wenlin, LAN Chunjiang
Complex Systems and Complexity Science. 2026, 23 (1): 87-95.   DOI: 10.13306/j.1672-3813.2026.01.011
Abstract ( 126 )     PDF (2689KB) ( 21 )  
For high aggregation networks, we proposed a new method KEC for identifying important nodes in complex networks, which considered both the local information of nodes and neighbors, that is, the influence factors, and the contribution degree of neighbors to the influence of nodes, and put forward the contribution factor. In eight real networks, the method used the SIR model and deliberate attack experiments to analyze the performance of KEC and six commonly used centrality. Finally, the method used the Kendall-tau correlation coefficient to analyze the correlation between the values of nodes calculated by KEC and six commonly used centrality. The results show that it is effective for KEC to identify influential node sets and improve the destruction resistance of networks, and the Kendall-tau correlation coefficients between KEC and six commonly used centrality are almost positively correlated in eight real networks, which shows that it is feasible for KEC to identify important nodes in complex networks.
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Urban Economic Flow Structure and Economic Energy Level Measurement from the Perspective of Multiplex Networks   Collect
SHI Yan, ZHANG Zili, ZHAO Xuejun
Complex Systems and Complexity Science. 2026, 23 (1): 96-103.   DOI: 10.13306/j.1672-3813.2026.01.012
Abstract ( 115 )     PDF (6106KB) ( 22 )  
To promote the coordinated and high-quality development of China's economy, this study combines the theory of flow-based economy and multiplex network analysis methods to construct a network model of material, capital, and technology information flow among cities. The entropy-based multi-attribute node importance measurement method is applied to propose a new framework for measuring the level of urban economy. Research shows that urban network structure is closely related to changes in macroeconomic conditions. The output results of the constructed economic level measurement model are consistent with authoritative survey reports, thus proving its effectiveness. Further studies reveal notable urban economic disparities across China's regions, with the east and the Yangtze River Delta in the lead. Positive trends emerged in the west and northeast due to policy guidance, but the central and Bohai Economic Circle still need more policy support. The flow of technological information is crucial for the upgrading of economic levels in economically developed regions. In contrast, the growth of levels in underdeveloped regions relies more on new capital investment.
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Evolutionary Game
Incentive Mechanisms for Green Transformation of Buildings Based on Communication Dynamics   Collect
FAN Chunmei, LI Xiaoyue
Complex Systems and Complexity Science. 2026, 23 (1): 104-113.   DOI: 10.13306/j.1672-3813.2026.01.013
Abstract ( 95 )     PDF (4695KB) ( 13 )  
To explore the mechanism of local government incentive policies on the supply and demand of green buildings, the study constructs the SEIR evolutionary game model based on the theory of evolutionary game and communication dynamics, exploring the game relationship between developers and local governments and the diffusion of green buildings among consumers under the different behavioral decisions of the two players. Research shows that green awareness exerts the most significant influence, and the diffusion of green buildings is maximized at the development stage as the level of stakeholders′ green awareness increases. In addition, the influence of local government behavior on green building diffusion is more significant than that of developers, and the incentive effect of subsidy policies is better than tax incentives.
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The Evolutionary Characteristics of Cultural Tourism Information Dissemination in the New Media Environment   Collect
ZHANG Jie, JIAN Lirong
Complex Systems and Complexity Science. 2026, 23 (1): 114-122.   DOI: 10.13306/j.1672-3813.2026.01.014
Abstract ( 114 )     PDF (1692KB) ( 24 )  
To study the evolutionary characteristics of cultural tourism information dissemination in the new media environment, analyze the impact of blogger promotion and host marketing on potential tourists, apply prospect theory to depict the profit and loss perception of bloggers and hosts in the process of cultural tourism information dissemination, comprehensively use SEIR and evolutionary game theory to construct a cultural tourism information dissemination model, and conduct numerical simulation with scenario cases in Xishuangbanna, Yunnan and Gaochun Old Street, Jiangsu. The research results indicate that, under a single information dissemination, the number of tourists follows an inverted U-shaped curve with the dissemination of cultural tourism information; The dissemination effect of cultural tourism information is positively correlated with the proportion of bloggers who choose communication strategies, the proportion of broadcasters who choose sales strategies, the number of contacts with communicators, the proportion of bloggers in the population, and the number of "fans" of bloggers, but negatively correlated with the duration of dissemination and natural attenuation parameters.
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Research Front
Disturbance-Compensation-Based Containment Control for Multiple Discrete-Time Euler-Lagrange Systems   Collect
GUO Xinchen, SONG Chuanming, LIANG Zhenying
Complex Systems and Complexity Science. 2026, 23 (1): 123-129.   DOI: 10.13306/j.1672-3813.2026.01.015
Abstract ( 118 )     PDF (2286KB) ( 18 )  
The containment control problem for multiple discrete-time Euler-Lagrange (EL for short) systems is studied in this paper. Firstly, the discrete-time EL system is transformed into a discrete-time second-order nonlinear system through the famous Euler’s first-order approximation method, and a local disturbance identifier is designed to estimate the compound disturbance for each EL system. Meanwhile, the tracking error dynamics are obtained by designing a state feedback controller involving both the available nonlinear term and the compensation of disturbances. Then, the finite-time boundedness and exponential ultimate boundedness of tracking errors are guaranteed, respectively, by selecting suitable controller gains. Finally, the effectiveness of the proposed control scheme is further verified by a numerical simulation of a group of two-link robotic arm systems.
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Efficient Multi-task Visual Perception Model in Autonomous Driving Scenarios   Collect
LIU Bohang, ZHAO Qiang, TANG Zhenglin, TANG Yinglong, LI Yeqi
Complex Systems and Complexity Science. 2026, 23 (1): 130-137.   DOI: 10.13306/j.1672-3813.2026.01.016
Abstract ( 115 )     PDF (6485KB) ( 19 )  
To efficiently utilize the hardware computing power of autonomous vehicles, a multi-task perception model OLAD is constructed based on YOLOv5,which can simultaneously achieve traffic object detection, lane lines recognition, and drivable area segmentation. By introducing an improved SPPFCSPC module and redesigning the feature fusion network based on Slim Neck, OLAD enhances feature extraction capabilities, inference speed, and detection accuracy, the loss function is improved by incorporating MPDIoU to boost the accuracy of traffic objects detection. In terms of model performance validation, a comprehensive performance evaluation is conducted by supplementing the self-made domestic road dataset in the BDD100K validation set. The results show that the detection accuracy and speed of OLAD are better than the YOLOP of SOTA; In addition, public road images from different time periods in Suzhou are randomly selected to test the performance of the model on domestic roads. The results show that the perception results of the OLAD model in this paper are more accurate and suitable for domestic roads.
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Integrating Local Relationships and Entities in Knowledge Graph Completion Model   Collect
GAO Rui, SUN Gengxin, BIN Sheng
Complex Systems and Complexity Science. 2026, 23 (1): 138-145.   DOI: 10.13306/j.1672-3813.2026.01.017
Abstract ( 122 )     PDF (4555KB) ( 20 )  
Given that the majority of existing knowledge graph completion methods adopt an independent processing approach for triplets, overlooking the varying contributions of neighborhood relations and entities to the central entity,this paper introduces a graph neural network model called REGNN that integrates neighborhood relations and entities. In this model, feature information from relations and entities within the neighborhood is incorporated into the central entity′s update, enriching the representation of the central entity through the aggregation of entity and relation features. Experimental results demonstrate that, in comparison to traditional graph neural network models, REGNN model achieves improvements of 3.3% and 1.5% in terms of the MMR and Hits@10 metrics on the FB15K-237 dataset, and improvements of 1.4% and 3.6% on the WN18RR dataset, thus validating the effectiveness of REGNN model.
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State Estimation of Boolean Control Networks Based on Control Inputs and State-flipped   Collect
XING Qian, YANG Junqi, WANG Shangkun
Complex Systems and Complexity Science. 2026, 23 (1): 146-152.   DOI: 10.13306/j.1672-3813.2026.01.018
Abstract ( 109 )     PDF (1434KB) ( 12 )  
In order to solve the state estimation problem of Boolean control networks, control inputs and state-flipped control are used in this paper. First, relying on the control inputs, the Boolean control network is transformed into a Boolean network, and then the state estimation problem of Boolean control network is studied based on the control inputs and outputs. Second, the state-flipped control is introduced to the system when the elements of the set of output-dependent state estimation are not unique, and a sufficient condition is proposed to realize the reachability of the target state. Third, all states in the output-dependent state estimation set are simultaneously flipped to the target state by designing an algorithm to calculate the joint control pair sequences, and further the state estimation of the Boolean control network is realized. Finally, it is shown through examples that the research method enables state estimation of Boolean control networks.
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Fixed-time Control of Nonlinear Systems with Full State Constraints Systems   Collect
GUO Qing,cAI Mingjie, WANG Baofanga,b
Complex Systems and Complexity Science. 2026, 23 (1): 153-159.   DOI: 10.13306/j.1672-3813.2026.01.019
Abstract ( 108 )     PDF (1756KB) ( 20 )  
A novel nonlinear mapping is introduced to address the fixed-time control problem of nonlinear systems with full state constraints, and a fixed-time control design method is proposed using the nonlinear mapping method. Firstly, We establish a mathematical model of a nonlinear system with full state constraints; Secondly, by combining time-varying state constraints and using nonlinear mapping techniques, the system with existing constraints is transformed into a corresponding unconstrained system; Then, a fixed-time control law based on backstepping is designed using a radial basis function neural network; Finally, the stability of the system is demonstrated using Lyapunov theory, and the effectiveness and feasibility of the proposed control method are verified through specific simulation examples.
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