The advent of sixth-generation(6G)networks introduces unprecedented challenges in achieving seamless connectivity,ultra-low latency,and efficient resource management in highly dynamic environments.Although fifth-gener...The advent of sixth-generation(6G)networks introduces unprecedented challenges in achieving seamless connectivity,ultra-low latency,and efficient resource management in highly dynamic environments.Although fifth-generation(5G)networks transformed mobile broadband and machine-type communications at massive scales,their properties of scaling,interference management,and latency remain a limitation in dense high mobility settings.To overcome these limitations,artificial intelligence(AI)and unmanned aerial vehicles(UAVs)have emerged as potential solutions to develop versatile,dynamic,and energy-efficient communication systems.The study proposes an AI-based UAV architecture that utilizes cooperative reinforcement learning(CoRL)to manage an autonomous network.The UAVs collaborate by sharing local observations and real-time state exchanges to optimize user connectivity,movement directions,allocate power,and resource distribution.Unlike conventional centralized or autonomous methods,CoRL involves joint state sharing and conflict-sensitive reward shaping,which ensures fair coverage,less interference,and enhanced adaptability in a dynamic urban environment.Simulations conducted in smart city scenarios with 10 UAVs and 50 ground users demonstrate that the proposed CoRL-based UAV system increases user coverage by up to 10%,achieves convergence 40%faster,and reduces latency and energy consumption by 30%compared with centralized and decentralized baselines.Furthermore,the distributed nature of the algorithm ensures scalability and flexibility,making it well-suited for future large-scale 6G deployments.The results highlighted that AI-enabled UAV systems enhance connectivity,support ultra-reliable low-latency communications(URLLC),and improve 6G network efficiency.Future work will extend the framework with adaptive modulation,beamforming-aware positioning,and real-world testbed deployment.展开更多
Wireless Sensor Networks(WSNs)have become foundational in numerous real-world applications,ranging from environmental monitoring and industrial automation to healthcare systems and smart city development.As these netw...Wireless Sensor Networks(WSNs)have become foundational in numerous real-world applications,ranging from environmental monitoring and industrial automation to healthcare systems and smart city development.As these networks continue to grow in scale and complexity,the need for energy-efficient,scalable,and robust communication protocols becomes more critical than ever.Metaheuristic algorithms have shown significant promise in addressing these challenges,offering flexible and effective solutions for optimizing WSN performance.Among them,the Grey Wolf Optimizer(GWO)algorithm has attracted growing attention due to its simplicity,fast convergence,and strong global search capabilities.Accordingly,this survey provides an in-depth review of the applications of GWO and its variants for clustering,multi-hop routing,and hybrid cluster-based routing in WSNs.We categorize and analyze the existing GWO-based approaches across these key network optimization tasks,discussing the different problem formulations,decision variables,objective functions,and performance metrics used.In doing so,we examine standard GWO,multi-objective GWO,and hybrid GWO models that incorporate other computational intelligence techniques.Each method is evaluated based on how effectively it addresses the core constraints of WSNs,including energy consumption,communication overhead,and network lifetime.Finally,this survey outlines existing gaps in the literature and proposes potential future research directions aimed at enhancing the effectiveness and real-world applicability of GWO-based techniques for WSN clustering and routing.Our goal is to provide researchers and practitioners with a clear,structured understanding of the current state of GWO in WSNs and inspire further innovation in this evolving field.展开更多
This paper investigates the traffic offloading optimization challenge in Space-Air-Ground Integrated Networks(SAGIN)through a novel Recursive Multi-Agent Proximal Policy Optimization(RMAPPO)algorithm.The exponential g...This paper investigates the traffic offloading optimization challenge in Space-Air-Ground Integrated Networks(SAGIN)through a novel Recursive Multi-Agent Proximal Policy Optimization(RMAPPO)algorithm.The exponential growth of mobile devices and data traffic has substantially increased network congestion,particularly in urban areas and regions with limited terrestrial infrastructure.Our approach jointly optimizes unmanned aerial vehicle(UAV)trajectories and satellite-assisted offloading strategies to simultaneously maximize data throughput,minimize energy consumption,and maintain equitable resource distribution.The proposed RMAPPO framework incorporates recurrent neural networks(RNNs)to model temporal dependencies in UAV mobility patterns and utilizes a decentralized multi-agent reinforcement learning architecture to reduce communication overhead while improving system robustness.The proposed RMAPPO algorithm was evaluated through simulation experiments,with the results indicating that it significantly enhances the cumulative traffic offloading rate of nodes and reduces the energy consumption of UAVs.展开更多
Internal structural defects in engineering rock masses vary in size,exhibit complex shapes,and are unevenly distributed.Dominant fractures within a rock mass often play a critical to its mechanical behavior,directly a...Internal structural defects in engineering rock masses vary in size,exhibit complex shapes,and are unevenly distributed.Dominant fractures within a rock mass often play a critical to its mechanical behavior,directly affecting the macromechanical properties and failure modes.These fractures affect the instability and failure of the surrounding rock,significantlyimpacting the overall stability of engineering structures.Herein,sand-powder three-dimensional(3D)printing technology was used to prepare rock-like specimens with internal fracture networks.Triaxial compression testing,post-failure fracture mapping,and fractal dimension analysis of the fracture surfaces were conducted to investigate the effects of dominant fracture angles on the strength and deformation of rocks with internal fracture networks under triaxial stress.The results indicate that the dominant fracture angle has a pronounced effect on the mechanical behavior of rock.With increasing angle,both compressive strength and elastic modulus exhibit an initial decline followed by an increase.Moreover,higher confiningpressure significantlyimproves the compressive strength of fractured rock.This enhancement weakens as the confiningpressure further increases.Moreover,with increasing confiningpressure,the differences between the maximum and minimum values of elastic moduli and lateral strain ratios in fractured rock gradually decrease.Thus,the impact of the dominant fracture angle on rock mass deformation decreases with increasing confiningpressure.This research elucidates the effects of dominant fracture angles on the mechanical and failure properties of complex fractured rock masses and the influenceof the confiningpressure on these relationships.It provides valuable theoretical insights and practical guidance for stability analyses in engineering rock masses.展开更多
Owing to intensified globalization and informatization,the structures of the urban scale hierarchy and urban networks between cities have become increasingly intertwined,resulting in different spatial effects.Therefor...Owing to intensified globalization and informatization,the structures of the urban scale hierarchy and urban networks between cities have become increasingly intertwined,resulting in different spatial effects.Therefore,this paper analyzes the spatial interaction between urban scale hierarchy and urban networks in China from 2019 to 2023,drawing on Baidu migration data and employing a spatial simultaneous equation model.The results reveal a significant positive spatial correlation between cities with higher hierarchy and those with greater network centrality.Within a static framework,we identify a positive interaction between urban scale hierarchy and urban network centrality,while their spatial cross-effects manifest as negative neighborhood interactions based on geographical distance and positive cross-scale interactions shaped by network connections.Within a dynamic framework,changes in urban scale hierarchy and urban networks are mutually reinforcing,thereby widening disparities within the urban hierarchy.Furthermore,an increase in a city’s network centrality had a dampening effect on the population growth of neighboring cities and network-connected cities.This study enhances understanding of the spatial organisation of urban systems and offers insights for coordinated regional development.展开更多
Optimizing routing and resource allocation in decentralized unmanned aerial vehicle(UAV)networks remains challenging due to interference and rapidly changing topologies.The authors introduce a novel framework combinin...Optimizing routing and resource allocation in decentralized unmanned aerial vehicle(UAV)networks remains challenging due to interference and rapidly changing topologies.The authors introduce a novel framework combining double deep Q-networks(DDQNs)and graph neural networks(GNNs)for joint routing and resource allocation.The framework uses GNNs to model the network topology and DDQNs to adaptively control routing and resource allocation,addressing interference and improving network performance.Simulation results show that the proposed approach outperforms traditional methods such as Closest-to-Destination(c2Dst),Max-SINR(mSINR),and Multi-Layer Perceptron(MLP)-based models,achieving approximately 23.5% improvement in throughput,50% increase in connection probability,and 17.6% reduction in number of hops,demonstrating its effectiveness in dynamic UAV networks.展开更多
Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may r...Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may represent underlying patterns and relationships.Networking structures are highly sensitive in social networks,requiring advanced techniques to accurately identify the structure of these communities.Most conventional algorithms for detecting communities perform inadequately with complicated networks.In addition,they miss out on accurately identifying clusters.Since single-objective optimization cannot always generate accurate and comprehensive results,as multi-objective optimization can.Therefore,we utilized two objective functions that enable strong connections between communities and weak connections between them.In this study,we utilized the intra function,which has proven effective in state-of-the-art research studies.We proposed a new inter-function that has demonstrated its effectiveness by making the objective of detecting external connections between communities is to make them more distinct and sparse.Furthermore,we proposed a Multi-Objective community strength enhancement algorithm(MOCSE).The proposed algorithm is based on the framework of the Multi-Objective Evolutionary Algorithm with Decomposition(MOEA/D),integrated with a new heuristic mutation strategy,community strength enhancement(CSE).The results demonstrate that the model is effective in accurately identifying community structures while also being computationally efficient.The performance measures used to evaluate the MOEA/D algorithm in our work are normalized mutual information(NMI)and modularity(Q).It was tested using five state-of-the-art algorithms on social networks,comprising real datasets(Zachary,Dolphin,Football,Krebs,SFI,Jazz,and Netscience),as well as twenty synthetic datasets.These results provide the robustness and practical value of the proposed algorithm in multi-objective community identification.展开更多
Skin diseases affect millions worldwide.Early detection is key to preventing disfigurement,lifelong disability,or death.Dermoscopic images acquired in primary-care settings show high intra-class visual similarity and ...Skin diseases affect millions worldwide.Early detection is key to preventing disfigurement,lifelong disability,or death.Dermoscopic images acquired in primary-care settings show high intra-class visual similarity and severe class imbalance,and occasional imaging artifacts can create ambiguity for state-of-the-art convolutional neural networks(CNNs).We frame skin lesion recognition as graph-based reasoning and,to ensure fair evaluation and avoid data leakage,adopt a strict lesion-level partitioning strategy.Each image is first over-segmented using SLIC(Simple Linear Iterative Clustering)to produce perceptually homogeneous superpixels.These superpixels form the nodes of a region-adjacency graph whose edges encode spatial continuity.Node attributes are 1280-dimensional embeddings extracted with a lightweight yet expressive EfficientNet-B0 backbone,providing strong representational power at modest computational cost.The resulting graphs are processed by a five-layer Graph Attention Network(GAT)that learns to weight inter-node relationships dynamically and aggregates multi-hop context before classifying lesions into seven classes with a log-softmax output.Extensive experiments on the DermaMNIST benchmark show the proposed pipeline achieves 88.35%accuracy and 98.04%AUC,outperforming contemporary CNNs,AutoML approaches,and alternative graph neural networks.An ablation study indicates EfficientNet-B0 produces superior node descriptors compared with ResNet-18 and DenseNet,and that roughly five GAT layers strike a good balance between being too shallow and over-deep while avoiding oversmoothing.The method requires no data augmentation or external metadata,making it a drop-in upgrade for clinical computer-aided diagnosis systems.展开更多
The rapid growth of distributed data-centric applications and AI workloads increases demand for low-latency,high-throughput communication,necessitating frequent and flexible updates to network routing configurations.H...The rapid growth of distributed data-centric applications and AI workloads increases demand for low-latency,high-throughput communication,necessitating frequent and flexible updates to network routing configurations.However,maintaining consistent forwarding states during these updates is challenging,particularly when rerouting multiple flows simultaneously.Existing approaches pay little attention to multi-flow update,where improper update sequences across data plane nodes may construct deadlock dependencies.Moreover,these methods typically involve excessive control-data plane interactions,incurring significant resource overhead and performance degradation.This paper presents P4LoF,an efficient loop-free update approach that enables the controller to reroute multiple flows through minimal interactions.P4LoF first utilizes a greedy-based algorithm to generate the shortest update dependency chain for the single-flow update.These chains are then dynamically merged into a dependency graph and resolved as a Shortest Common Super-sequence(SCS)problem to produce the update sequence of multi-flow update.To address deadlock dependencies in multi-flow updates,P4LoF builds a deadlock-fix forwarding model that leverages the flexible packet processing capabilities of the programmable data plane.Experimental results show that P4LoF reduces control-data plane interactions by at least 32.6%with modest overhead,while effectively guaranteeing loop-free consistency.展开更多
The adjoint method is widely used in gradient-based optimization with high-dimensional design variables.However,the cost of solving the adjoint equations in each iteration is comparable to that of solving the flow fie...The adjoint method is widely used in gradient-based optimization with high-dimensional design variables.However,the cost of solving the adjoint equations in each iteration is comparable to that of solving the flow field,resulting in expensive computational costs.To improve the efficiency of solving adjoint equations,we propose a physics-constrained graph neural networks for solving adjoint equations,named ADJ-PCGN.ADJ-PCGN establishes a mapping relationship between flow characteristics and adjoint vector based on data,serving as a replacement for the computationally expensive numerical solution of adjoint equations.A physics-based graph structure and message-passing mechanism are designed to endow its strong fitting and generalization capabilities.Taking transonic drag reduction and maximum lift-drag ratio of the airfoil as examples,results indicate that ADJ-PCGN attains a similar optimal shape as the classical direct adjoint loop method.In addition,ADJ-PCGN demonstrates strong generalization capabilities across different mesh topologies,mesh densities,and out-of-distribution conditions.It holds the potential to become a universal model for aerodynamic shape optimization involving states,geometries,and meshes.展开更多
Ensuring reliable power supply in urban distribution networks is a complex and critical task.To address the increased demand during extreme scenarios,this paper proposes an optimal dispatch strategy that considers the...Ensuring reliable power supply in urban distribution networks is a complex and critical task.To address the increased demand during extreme scenarios,this paper proposes an optimal dispatch strategy that considers the coordination with virtual power plants(VPPs).The proposed strategy improves systemflexibility and responsiveness by optimizing the power adjustment of flexible resources.In the proposed strategy,theGaussian Process Regression(GPR)is firstly employed to determine the adjustable range of aggregated power within the VPP,facilitating an assessment of its potential contribution to power supply support.Then,an optimal dispatch model based on a leader-follower game is developed to maximize the benefits of the VPP and flexible resources while guaranteeing the power balance at the same time.To solve the proposed optimal dispatch model efficiently,the constraints of the problem are reformulated and resolved using the Karush-Kuhn-Tucker(KKT)optimality conditions and linear programming duality theorem.The effectiveness of the strategy is illustrated through a detailed case study.展开更多
Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performan...Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performance of PINNs in solving the temperature diffusion equation of the seawater across six scenarios,including forward and inverse problems under three different boundary conditions.Results demonstrate that PINNs achieved consistently higher accuracy with the Dirichlet and Neumann boundary conditions compared to the Robin boundary condition for both forward and inverse problems.Inaccurate weighting of terms in the loss function can reduce model accuracy.Additionally,the sensitivity of model performance to the positioning of sampling points varied between different boundary conditions.In particular,the model under the Dirichlet boundary condition exhibited superior robustness to variations in point positions during the solutions of inverse problems.In contrast,for the Neumann and Robin boundary conditions,accuracy declines when points were sampled from identical positions or at the same time.Subsequently,the Argo observations were used to reconstruct the vertical diffusion of seawater temperature in the north-central Pacific for the applicability of PINNs in the real ocean.The PINNs successfully captured the vertical diffusion characteristics of seawater temperature,reflected the seasonal changes of vertical temperature under different topographic conditions,and revealed the influence of topography on the temperature diffusion coefficient.The PINNs were proved effective in solving the temperature diffusion equation of seawater with limited data,providing a promising technique for simulating or predicting ocean phenomena using sparse observations.展开更多
This study proposes a novel forecasting framework that simultaneously captures the strong periodicity and irregular meteorological fluctuations inherent in solar radiation time series.Existing approaches typically def...This study proposes a novel forecasting framework that simultaneously captures the strong periodicity and irregular meteorological fluctuations inherent in solar radiation time series.Existing approaches typically define inter-regional correlations using either simple correlation coefficients or distance-based measures when applying spatio-temporal graph neural networks(STGNNs).However,such definitions are prone to generating spurious correlations due to the dominance of periodic structures.To address this limitation,we adopt the Elastic-Band Transform(EBT)to decompose solar radiation into periodic and amplitude-modulated components,which are then modeled independently with separate graph neural networks.The periodic component,characterized by strong nationwide correlations,is learned with a relatively simple architecture,whereas the amplitude-modulated component is modeled with more complex STGNNs that capture climatological similarities between regions.The predictions from the two components are subsequently recombined to yield final forecasts that integrate both periodic patterns and aperiodic variability.The proposed framework is validated with multiple STGNN architectures,and experimental results demonstrate improved predictive accuracy and interpretability compared to conventional methods.展开更多
Fractures are typically characterized by roughness that significantlyaffects the mechanical and hydraulic characteristics of reservoirs.However,hydraulic fracturing mechanisms under the influenceof fracture morphology...Fractures are typically characterized by roughness that significantlyaffects the mechanical and hydraulic characteristics of reservoirs.However,hydraulic fracturing mechanisms under the influenceof fracture morphology remain largely unexplored.Leveraging the advantages of the finite-discrete element method(FDEM)for explicitly simulating fracture propagation and the strengths of the unifiedpipe model(UPM)for efficientlymodeling dual-permeability seepage,we propose a new hydromechanical(HM)coupling approach for modeling hydraulic fracturing.Validated against benchmark examples,the proposed FDEM-UPM model is further augmented by incorporating a Fourier-based methodology for reconstructing non-planar fractures,enabling quantitative analysis of hydraulic fracturing behavior within rough discrete fracture networks(DFNs).The FDEM-UPM model demonstrates computational advantages in accurately capturing transient hydraulic seepage phenomena,while the asynchronous time-stepping schemes between hydraulic and mechanical analyses substantially enhanced computational efficiencywithout compromising computational accuracy.Our results show that fracture morphology can affect both macroscopic fracture networks and microscopic interaction types between hydraulic fractures(HFs)and natural fractures(NFs).In an isotropic stress field,the initiation azimuth,propagation direction and microcracking mechanism are significantly influencedby fracture roughness.In an anisotropic stress field,HFs invariably propagate parallel to the direction of the maximum principal stress,reducing the overall complexity of the stimulated fracture networks.Additionally,stress concentration and perturbation attributed to fracture morphology tend to be compromised as the leak-off increases,while the breakdown and propagation pressures remain insensitive to fracture morphology.These findingsprovide new insights into the hydraulic fracturing mechanisms of fractured reservoirs containing complex rough DFNs.展开更多
With the emphasis on user privacy and communication security, encrypted traffic has increased dramatically, which brings great challenges to traffic classification. The classification method of encrypted traffic based...With the emphasis on user privacy and communication security, encrypted traffic has increased dramatically, which brings great challenges to traffic classification. The classification method of encrypted traffic based on GNN can deal with encrypted traffic well. However, existing GNN-based approaches ignore the relationship between client or server packets. In this paper, we design a network traffic topology based on GCN, called Flow Mapping Graph (FMG). FMG establishes sequential edges between vertexes by the arrival order of packets and establishes jump-order edges between vertexes by connecting packets in different bursts with the same direction. It not only reflects the time characteristics of the packet but also strengthens the relationship between the client or server packets. According to FMG, a Traffic Mapping Classification model (TMC-GCN) is designed, which can automatically capture and learn the characteristics and structure information of the top vertex in FMG. The TMC-GCN model is used to classify the encrypted traffic. The encryption stream classification problem is transformed into a graph classification problem, which can effectively deal with data from different data sources and application scenarios. By comparing the performance of TMC-GCN with other classical models in four public datasets, including CICIOT2023, ISCXVPN2016, CICAAGM2017, and GraphDapp, the effectiveness of the FMG algorithm is verified. The experimental results show that the accuracy rate of the TMC-GCN model is 96.13%, the recall rate is 95.04%, and the F1 rate is 94.54%.展开更多
The increasing popularity of the Internet and the widespread use of information technology have led to a rise in the number and sophistication of network attacks and security threats.Intrusion detection systems are cr...The increasing popularity of the Internet and the widespread use of information technology have led to a rise in the number and sophistication of network attacks and security threats.Intrusion detection systems are crucial to network security,playing a pivotal role in safeguarding networks from potential threats.However,in the context of an evolving landscape of sophisticated and elusive attacks,existing intrusion detection methodologies often overlook critical aspects such as changes in network topology over time and interactions between hosts.To address these issues,this paper proposes a real-time network intrusion detection method based on graph neural networks.The proposedmethod leverages the advantages of graph neural networks and employs a straightforward graph construction method to represent network traffic as dynamic graph-structured data.Additionally,a graph convolution operation with a multi-head attention mechanism is utilized to enhance the model’s ability to capture the intricate relationships within the graph structure comprehensively.Furthermore,it uses an integrated graph neural network to address dynamic graphs’structural and topological changes at different time points and the challenges of edge embedding in intrusion detection data.The edge classification problem is effectively transformed into node classification by employing a line graph data representation,which facilitates fine-grained intrusion detection tasks on dynamic graph node feature representations.The efficacy of the proposed method is evaluated using two commonly used intrusion detection datasets,UNSW-NB15 and NF-ToN-IoT-v2,and results are compared with previous studies in this field.The experimental results demonstrate that our proposed method achieves 99.3%and 99.96%accuracy on the two datasets,respectively,and outperforms the benchmark model in several evaluation metrics.展开更多
This paper proposes a model-based control framework for vehicle platooning systems with secondorder nonlinear dynamics operating over switching signed networks,time-varying delays,and deception attacks.The study inclu...This paper proposes a model-based control framework for vehicle platooning systems with secondorder nonlinear dynamics operating over switching signed networks,time-varying delays,and deception attacks.The study includes two configurations:a leaderless structure using Finite-Time Non-Singular Terminal Bipartite Consensus(FNTBC)and Fixed-Time Bipartite Consensus(FXTBC),and a leader—follower structure ensuring structural balance and robustness against deceptive signals.In the leaderless model,a bipartite controller based on impulsive control theory,gauge transformation,and Markovian switching Lyapunov functions ensures mean-square stability and coordination under deception attacks and communication delays.The FNTBC achieves finite-time convergence depending on initial conditions,while the FXTBC guarantees fixed-time convergence independent of them,providing adaptability to different operating states.In the leader—follower case,a discontinuous impulsive control law synchronizes all followers with the leader despite deceptive attacks and switching topologies,maintaining robust coordination through nonlinear corrective mechanisms.To validate the approach,simulations are conducted on systems of five and seventeen vehicles in both leaderless and leader—follower configurations.The results demonstrate that the proposed framework achieves rapid consensus,strong robustness,and high resistance to deception attacks,offering a secure and scalable model-based control solution for modern vehicular communication networks.展开更多
Dear Editor,This letter proposes a dynamic switching soft slicing strategy for industrial mixed traffic in 5G networks. Considering two types of traffic, periodic delay-sensitive (PDS) traffic and sporadic delay-toler...Dear Editor,This letter proposes a dynamic switching soft slicing strategy for industrial mixed traffic in 5G networks. Considering two types of traffic, periodic delay-sensitive (PDS) traffic and sporadic delay-tolerant (SDT) traffic, we design a dynamic switching strategy based on a traffic-Qo S-aware soft slicing (TQASS) scheme and a resource-efficiency-aware soft slicing (REASS) scheme.展开更多
Friendship paradox states that individuals are likely to have fewer friends than their friends do,on average.Despite of its wide existence and appealing applications in real social networks,the mathematical understand...Friendship paradox states that individuals are likely to have fewer friends than their friends do,on average.Despite of its wide existence and appealing applications in real social networks,the mathematical understanding of friendship paradox is very limited.Only few works provide theoretical evidence of single-step and multi-step friendship paradoxes,given that the neighbors of interest are onehop and multi-hop away from the target node.However,they consider non-evolving networks,as opposed to the topology of real social networks that are constantly growing over time.We are thus motivated to present a first look into friendship paradox in evolving networks,where newly added nodes preferentially attach themselves to those with higher degrees.Our analytical verification of both single-step and multistep friendship paradoxes in evolving networks,along with comparison to the non-evolving counterparts,discloses that“friendship paradox is even more paradoxical in evolving networks”,primarily from three aspects:1)we demonstrate a strengthened effect of single-step friendship paradox in evolving networks,with a larger probability(more than 0.8)of a random node’s neighbors having higher average degree than the random node itself;2)we unravel higher effectiveness of multi-step friendship paradox in seeking for influential nodes in evolving networks,as the rate of reaching the max degree node can be improved by a factor of at least Θ(t^(2/3))with t being the network size;3)we empirically verify our findings through both synthetic and real datasets,which suggest high agreements of results and consolidate the reasonability of evolving model for real social networks.展开更多
基金supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(RS-2025-00559546)supported by the IITP(Institute of Information&Coummunications Technology Planning&Evaluation)-ITRC(Information Technology Research Center)grant funded by the Korea government(Ministry of Science and ICT)(IITP-2025-RS-2023-00259004).
文摘The advent of sixth-generation(6G)networks introduces unprecedented challenges in achieving seamless connectivity,ultra-low latency,and efficient resource management in highly dynamic environments.Although fifth-generation(5G)networks transformed mobile broadband and machine-type communications at massive scales,their properties of scaling,interference management,and latency remain a limitation in dense high mobility settings.To overcome these limitations,artificial intelligence(AI)and unmanned aerial vehicles(UAVs)have emerged as potential solutions to develop versatile,dynamic,and energy-efficient communication systems.The study proposes an AI-based UAV architecture that utilizes cooperative reinforcement learning(CoRL)to manage an autonomous network.The UAVs collaborate by sharing local observations and real-time state exchanges to optimize user connectivity,movement directions,allocate power,and resource distribution.Unlike conventional centralized or autonomous methods,CoRL involves joint state sharing and conflict-sensitive reward shaping,which ensures fair coverage,less interference,and enhanced adaptability in a dynamic urban environment.Simulations conducted in smart city scenarios with 10 UAVs and 50 ground users demonstrate that the proposed CoRL-based UAV system increases user coverage by up to 10%,achieves convergence 40%faster,and reduces latency and energy consumption by 30%compared with centralized and decentralized baselines.Furthermore,the distributed nature of the algorithm ensures scalability and flexibility,making it well-suited for future large-scale 6G deployments.The results highlighted that AI-enabled UAV systems enhance connectivity,support ultra-reliable low-latency communications(URLLC),and improve 6G network efficiency.Future work will extend the framework with adaptive modulation,beamforming-aware positioning,and real-world testbed deployment.
文摘Wireless Sensor Networks(WSNs)have become foundational in numerous real-world applications,ranging from environmental monitoring and industrial automation to healthcare systems and smart city development.As these networks continue to grow in scale and complexity,the need for energy-efficient,scalable,and robust communication protocols becomes more critical than ever.Metaheuristic algorithms have shown significant promise in addressing these challenges,offering flexible and effective solutions for optimizing WSN performance.Among them,the Grey Wolf Optimizer(GWO)algorithm has attracted growing attention due to its simplicity,fast convergence,and strong global search capabilities.Accordingly,this survey provides an in-depth review of the applications of GWO and its variants for clustering,multi-hop routing,and hybrid cluster-based routing in WSNs.We categorize and analyze the existing GWO-based approaches across these key network optimization tasks,discussing the different problem formulations,decision variables,objective functions,and performance metrics used.In doing so,we examine standard GWO,multi-objective GWO,and hybrid GWO models that incorporate other computational intelligence techniques.Each method is evaluated based on how effectively it addresses the core constraints of WSNs,including energy consumption,communication overhead,and network lifetime.Finally,this survey outlines existing gaps in the literature and proposes potential future research directions aimed at enhancing the effectiveness and real-world applicability of GWO-based techniques for WSN clustering and routing.Our goal is to provide researchers and practitioners with a clear,structured understanding of the current state of GWO in WSNs and inspire further innovation in this evolving field.
文摘This paper investigates the traffic offloading optimization challenge in Space-Air-Ground Integrated Networks(SAGIN)through a novel Recursive Multi-Agent Proximal Policy Optimization(RMAPPO)algorithm.The exponential growth of mobile devices and data traffic has substantially increased network congestion,particularly in urban areas and regions with limited terrestrial infrastructure.Our approach jointly optimizes unmanned aerial vehicle(UAV)trajectories and satellite-assisted offloading strategies to simultaneously maximize data throughput,minimize energy consumption,and maintain equitable resource distribution.The proposed RMAPPO framework incorporates recurrent neural networks(RNNs)to model temporal dependencies in UAV mobility patterns and utilizes a decentralized multi-agent reinforcement learning architecture to reduce communication overhead while improving system robustness.The proposed RMAPPO algorithm was evaluated through simulation experiments,with the results indicating that it significantly enhances the cumulative traffic offloading rate of nodes and reduces the energy consumption of UAVs.
基金supported by the National Key Research and Development Program Young Scientist Project(Grant No.2024YFC2911000)the National Natural Science Foundation of China(Grant No.52474103)the Major Basic Research Project of the Natural Science Foundation of Shandong Province(Grant No.ZR2024ZD22).
文摘Internal structural defects in engineering rock masses vary in size,exhibit complex shapes,and are unevenly distributed.Dominant fractures within a rock mass often play a critical to its mechanical behavior,directly affecting the macromechanical properties and failure modes.These fractures affect the instability and failure of the surrounding rock,significantlyimpacting the overall stability of engineering structures.Herein,sand-powder three-dimensional(3D)printing technology was used to prepare rock-like specimens with internal fracture networks.Triaxial compression testing,post-failure fracture mapping,and fractal dimension analysis of the fracture surfaces were conducted to investigate the effects of dominant fracture angles on the strength and deformation of rocks with internal fracture networks under triaxial stress.The results indicate that the dominant fracture angle has a pronounced effect on the mechanical behavior of rock.With increasing angle,both compressive strength and elastic modulus exhibit an initial decline followed by an increase.Moreover,higher confiningpressure significantlyimproves the compressive strength of fractured rock.This enhancement weakens as the confiningpressure further increases.Moreover,with increasing confiningpressure,the differences between the maximum and minimum values of elastic moduli and lateral strain ratios in fractured rock gradually decrease.Thus,the impact of the dominant fracture angle on rock mass deformation decreases with increasing confiningpressure.This research elucidates the effects of dominant fracture angles on the mechanical and failure properties of complex fractured rock masses and the influenceof the confiningpressure on these relationships.It provides valuable theoretical insights and practical guidance for stability analyses in engineering rock masses.
基金Under the auspices of the National Natural Science Foundation of China(No.42371222,41971167)Fundamental Scientific Research Funds of Central China Normal University(No.CCNU24ZZ120)。
文摘Owing to intensified globalization and informatization,the structures of the urban scale hierarchy and urban networks between cities have become increasingly intertwined,resulting in different spatial effects.Therefore,this paper analyzes the spatial interaction between urban scale hierarchy and urban networks in China from 2019 to 2023,drawing on Baidu migration data and employing a spatial simultaneous equation model.The results reveal a significant positive spatial correlation between cities with higher hierarchy and those with greater network centrality.Within a static framework,we identify a positive interaction between urban scale hierarchy and urban network centrality,while their spatial cross-effects manifest as negative neighborhood interactions based on geographical distance and positive cross-scale interactions shaped by network connections.Within a dynamic framework,changes in urban scale hierarchy and urban networks are mutually reinforcing,thereby widening disparities within the urban hierarchy.Furthermore,an increase in a city’s network centrality had a dampening effect on the population growth of neighboring cities and network-connected cities.This study enhances understanding of the spatial organisation of urban systems and offers insights for coordinated regional development.
文摘Optimizing routing and resource allocation in decentralized unmanned aerial vehicle(UAV)networks remains challenging due to interference and rapidly changing topologies.The authors introduce a novel framework combining double deep Q-networks(DDQNs)and graph neural networks(GNNs)for joint routing and resource allocation.The framework uses GNNs to model the network topology and DDQNs to adaptively control routing and resource allocation,addressing interference and improving network performance.Simulation results show that the proposed approach outperforms traditional methods such as Closest-to-Destination(c2Dst),Max-SINR(mSINR),and Multi-Layer Perceptron(MLP)-based models,achieving approximately 23.5% improvement in throughput,50% increase in connection probability,and 17.6% reduction in number of hops,demonstrating its effectiveness in dynamic UAV networks.
文摘Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may represent underlying patterns and relationships.Networking structures are highly sensitive in social networks,requiring advanced techniques to accurately identify the structure of these communities.Most conventional algorithms for detecting communities perform inadequately with complicated networks.In addition,they miss out on accurately identifying clusters.Since single-objective optimization cannot always generate accurate and comprehensive results,as multi-objective optimization can.Therefore,we utilized two objective functions that enable strong connections between communities and weak connections between them.In this study,we utilized the intra function,which has proven effective in state-of-the-art research studies.We proposed a new inter-function that has demonstrated its effectiveness by making the objective of detecting external connections between communities is to make them more distinct and sparse.Furthermore,we proposed a Multi-Objective community strength enhancement algorithm(MOCSE).The proposed algorithm is based on the framework of the Multi-Objective Evolutionary Algorithm with Decomposition(MOEA/D),integrated with a new heuristic mutation strategy,community strength enhancement(CSE).The results demonstrate that the model is effective in accurately identifying community structures while also being computationally efficient.The performance measures used to evaluate the MOEA/D algorithm in our work are normalized mutual information(NMI)and modularity(Q).It was tested using five state-of-the-art algorithms on social networks,comprising real datasets(Zachary,Dolphin,Football,Krebs,SFI,Jazz,and Netscience),as well as twenty synthetic datasets.These results provide the robustness and practical value of the proposed algorithm in multi-objective community identification.
基金funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under grant No.(DGSSR-2025-02-01296).
文摘Skin diseases affect millions worldwide.Early detection is key to preventing disfigurement,lifelong disability,or death.Dermoscopic images acquired in primary-care settings show high intra-class visual similarity and severe class imbalance,and occasional imaging artifacts can create ambiguity for state-of-the-art convolutional neural networks(CNNs).We frame skin lesion recognition as graph-based reasoning and,to ensure fair evaluation and avoid data leakage,adopt a strict lesion-level partitioning strategy.Each image is first over-segmented using SLIC(Simple Linear Iterative Clustering)to produce perceptually homogeneous superpixels.These superpixels form the nodes of a region-adjacency graph whose edges encode spatial continuity.Node attributes are 1280-dimensional embeddings extracted with a lightweight yet expressive EfficientNet-B0 backbone,providing strong representational power at modest computational cost.The resulting graphs are processed by a five-layer Graph Attention Network(GAT)that learns to weight inter-node relationships dynamically and aggregates multi-hop context before classifying lesions into seven classes with a log-softmax output.Extensive experiments on the DermaMNIST benchmark show the proposed pipeline achieves 88.35%accuracy and 98.04%AUC,outperforming contemporary CNNs,AutoML approaches,and alternative graph neural networks.An ablation study indicates EfficientNet-B0 produces superior node descriptors compared with ResNet-18 and DenseNet,and that roughly five GAT layers strike a good balance between being too shallow and over-deep while avoiding oversmoothing.The method requires no data augmentation or external metadata,making it a drop-in upgrade for clinical computer-aided diagnosis systems.
基金supported by the National Key Research and Development Program of China under Grant 2022YFB2901501in part by the Science and Technology Innovation leading Talents Subsidy Project of Central Plains under Grant 244200510038.
文摘The rapid growth of distributed data-centric applications and AI workloads increases demand for low-latency,high-throughput communication,necessitating frequent and flexible updates to network routing configurations.However,maintaining consistent forwarding states during these updates is challenging,particularly when rerouting multiple flows simultaneously.Existing approaches pay little attention to multi-flow update,where improper update sequences across data plane nodes may construct deadlock dependencies.Moreover,these methods typically involve excessive control-data plane interactions,incurring significant resource overhead and performance degradation.This paper presents P4LoF,an efficient loop-free update approach that enables the controller to reroute multiple flows through minimal interactions.P4LoF first utilizes a greedy-based algorithm to generate the shortest update dependency chain for the single-flow update.These chains are then dynamically merged into a dependency graph and resolved as a Shortest Common Super-sequence(SCS)problem to produce the update sequence of multi-flow update.To address deadlock dependencies in multi-flow updates,P4LoF builds a deadlock-fix forwarding model that leverages the flexible packet processing capabilities of the programmable data plane.Experimental results show that P4LoF reduces control-data plane interactions by at least 32.6%with modest overhead,while effectively guaranteeing loop-free consistency.
基金supported by the National Natural Science Foundation of China(Grant No.12272316).
文摘The adjoint method is widely used in gradient-based optimization with high-dimensional design variables.However,the cost of solving the adjoint equations in each iteration is comparable to that of solving the flow field,resulting in expensive computational costs.To improve the efficiency of solving adjoint equations,we propose a physics-constrained graph neural networks for solving adjoint equations,named ADJ-PCGN.ADJ-PCGN establishes a mapping relationship between flow characteristics and adjoint vector based on data,serving as a replacement for the computationally expensive numerical solution of adjoint equations.A physics-based graph structure and message-passing mechanism are designed to endow its strong fitting and generalization capabilities.Taking transonic drag reduction and maximum lift-drag ratio of the airfoil as examples,results indicate that ADJ-PCGN attains a similar optimal shape as the classical direct adjoint loop method.In addition,ADJ-PCGN demonstrates strong generalization capabilities across different mesh topologies,mesh densities,and out-of-distribution conditions.It holds the potential to become a universal model for aerodynamic shape optimization involving states,geometries,and meshes.
基金supported by the Science and Technology Project of Sichuan Electric Power Company“Power Supply Guarantee Strategy for Urban Distribution Networks Considering Coordination with Virtual Power Plant during Extreme Weather Event”(No.521920230003).
文摘Ensuring reliable power supply in urban distribution networks is a complex and critical task.To address the increased demand during extreme scenarios,this paper proposes an optimal dispatch strategy that considers the coordination with virtual power plants(VPPs).The proposed strategy improves systemflexibility and responsiveness by optimizing the power adjustment of flexible resources.In the proposed strategy,theGaussian Process Regression(GPR)is firstly employed to determine the adjustable range of aggregated power within the VPP,facilitating an assessment of its potential contribution to power supply support.Then,an optimal dispatch model based on a leader-follower game is developed to maximize the benefits of the VPP and flexible resources while guaranteeing the power balance at the same time.To solve the proposed optimal dispatch model efficiently,the constraints of the problem are reformulated and resolved using the Karush-Kuhn-Tucker(KKT)optimality conditions and linear programming duality theorem.The effectiveness of the strategy is illustrated through a detailed case study.
基金Supported by the National Key Research and Development Program of China(No.2023YFC3008200)the Independent Research Project of Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(No.SML2022SP505)。
文摘Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performance of PINNs in solving the temperature diffusion equation of the seawater across six scenarios,including forward and inverse problems under three different boundary conditions.Results demonstrate that PINNs achieved consistently higher accuracy with the Dirichlet and Neumann boundary conditions compared to the Robin boundary condition for both forward and inverse problems.Inaccurate weighting of terms in the loss function can reduce model accuracy.Additionally,the sensitivity of model performance to the positioning of sampling points varied between different boundary conditions.In particular,the model under the Dirichlet boundary condition exhibited superior robustness to variations in point positions during the solutions of inverse problems.In contrast,for the Neumann and Robin boundary conditions,accuracy declines when points were sampled from identical positions or at the same time.Subsequently,the Argo observations were used to reconstruct the vertical diffusion of seawater temperature in the north-central Pacific for the applicability of PINNs in the real ocean.The PINNs successfully captured the vertical diffusion characteristics of seawater temperature,reflected the seasonal changes of vertical temperature under different topographic conditions,and revealed the influence of topography on the temperature diffusion coefficient.The PINNs were proved effective in solving the temperature diffusion equation of seawater with limited data,providing a promising technique for simulating or predicting ocean phenomena using sparse observations.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(RS-2023-00249743).
文摘This study proposes a novel forecasting framework that simultaneously captures the strong periodicity and irregular meteorological fluctuations inherent in solar radiation time series.Existing approaches typically define inter-regional correlations using either simple correlation coefficients or distance-based measures when applying spatio-temporal graph neural networks(STGNNs).However,such definitions are prone to generating spurious correlations due to the dominance of periodic structures.To address this limitation,we adopt the Elastic-Band Transform(EBT)to decompose solar radiation into periodic and amplitude-modulated components,which are then modeled independently with separate graph neural networks.The periodic component,characterized by strong nationwide correlations,is learned with a relatively simple architecture,whereas the amplitude-modulated component is modeled with more complex STGNNs that capture climatological similarities between regions.The predictions from the two components are subsequently recombined to yield final forecasts that integrate both periodic patterns and aperiodic variability.The proposed framework is validated with multiple STGNN architectures,and experimental results demonstrate improved predictive accuracy and interpretability compared to conventional methods.
基金supported by the National Natural Science Foundation of China(Grant Nos.52574103 and 42277150).
文摘Fractures are typically characterized by roughness that significantlyaffects the mechanical and hydraulic characteristics of reservoirs.However,hydraulic fracturing mechanisms under the influenceof fracture morphology remain largely unexplored.Leveraging the advantages of the finite-discrete element method(FDEM)for explicitly simulating fracture propagation and the strengths of the unifiedpipe model(UPM)for efficientlymodeling dual-permeability seepage,we propose a new hydromechanical(HM)coupling approach for modeling hydraulic fracturing.Validated against benchmark examples,the proposed FDEM-UPM model is further augmented by incorporating a Fourier-based methodology for reconstructing non-planar fractures,enabling quantitative analysis of hydraulic fracturing behavior within rough discrete fracture networks(DFNs).The FDEM-UPM model demonstrates computational advantages in accurately capturing transient hydraulic seepage phenomena,while the asynchronous time-stepping schemes between hydraulic and mechanical analyses substantially enhanced computational efficiencywithout compromising computational accuracy.Our results show that fracture morphology can affect both macroscopic fracture networks and microscopic interaction types between hydraulic fractures(HFs)and natural fractures(NFs).In an isotropic stress field,the initiation azimuth,propagation direction and microcracking mechanism are significantly influencedby fracture roughness.In an anisotropic stress field,HFs invariably propagate parallel to the direction of the maximum principal stress,reducing the overall complexity of the stimulated fracture networks.Additionally,stress concentration and perturbation attributed to fracture morphology tend to be compromised as the leak-off increases,while the breakdown and propagation pressures remain insensitive to fracture morphology.These findingsprovide new insights into the hydraulic fracturing mechanisms of fractured reservoirs containing complex rough DFNs.
基金supported by the National Key Research and Development Program of China No.2023YFA1009500.
文摘With the emphasis on user privacy and communication security, encrypted traffic has increased dramatically, which brings great challenges to traffic classification. The classification method of encrypted traffic based on GNN can deal with encrypted traffic well. However, existing GNN-based approaches ignore the relationship between client or server packets. In this paper, we design a network traffic topology based on GCN, called Flow Mapping Graph (FMG). FMG establishes sequential edges between vertexes by the arrival order of packets and establishes jump-order edges between vertexes by connecting packets in different bursts with the same direction. It not only reflects the time characteristics of the packet but also strengthens the relationship between the client or server packets. According to FMG, a Traffic Mapping Classification model (TMC-GCN) is designed, which can automatically capture and learn the characteristics and structure information of the top vertex in FMG. The TMC-GCN model is used to classify the encrypted traffic. The encryption stream classification problem is transformed into a graph classification problem, which can effectively deal with data from different data sources and application scenarios. By comparing the performance of TMC-GCN with other classical models in four public datasets, including CICIOT2023, ISCXVPN2016, CICAAGM2017, and GraphDapp, the effectiveness of the FMG algorithm is verified. The experimental results show that the accuracy rate of the TMC-GCN model is 96.13%, the recall rate is 95.04%, and the F1 rate is 94.54%.
文摘The increasing popularity of the Internet and the widespread use of information technology have led to a rise in the number and sophistication of network attacks and security threats.Intrusion detection systems are crucial to network security,playing a pivotal role in safeguarding networks from potential threats.However,in the context of an evolving landscape of sophisticated and elusive attacks,existing intrusion detection methodologies often overlook critical aspects such as changes in network topology over time and interactions between hosts.To address these issues,this paper proposes a real-time network intrusion detection method based on graph neural networks.The proposedmethod leverages the advantages of graph neural networks and employs a straightforward graph construction method to represent network traffic as dynamic graph-structured data.Additionally,a graph convolution operation with a multi-head attention mechanism is utilized to enhance the model’s ability to capture the intricate relationships within the graph structure comprehensively.Furthermore,it uses an integrated graph neural network to address dynamic graphs’structural and topological changes at different time points and the challenges of edge embedding in intrusion detection data.The edge classification problem is effectively transformed into node classification by employing a line graph data representation,which facilitates fine-grained intrusion detection tasks on dynamic graph node feature representations.The efficacy of the proposed method is evaluated using two commonly used intrusion detection datasets,UNSW-NB15 and NF-ToN-IoT-v2,and results are compared with previous studies in this field.The experimental results demonstrate that our proposed method achieves 99.3%and 99.96%accuracy on the two datasets,respectively,and outperforms the benchmark model in several evaluation metrics.
基金Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP.2/103/46”Deanship of Scientific Research at Northern Border University,Arar,Saudi Arabia for funding this research work through project number“NBU-FFR-2025-871-15”funding from Prince Sattam bin Abdulaziz University project number(PSAU/2025/R/1447).
文摘This paper proposes a model-based control framework for vehicle platooning systems with secondorder nonlinear dynamics operating over switching signed networks,time-varying delays,and deception attacks.The study includes two configurations:a leaderless structure using Finite-Time Non-Singular Terminal Bipartite Consensus(FNTBC)and Fixed-Time Bipartite Consensus(FXTBC),and a leader—follower structure ensuring structural balance and robustness against deceptive signals.In the leaderless model,a bipartite controller based on impulsive control theory,gauge transformation,and Markovian switching Lyapunov functions ensures mean-square stability and coordination under deception attacks and communication delays.The FNTBC achieves finite-time convergence depending on initial conditions,while the FXTBC guarantees fixed-time convergence independent of them,providing adaptability to different operating states.In the leader—follower case,a discontinuous impulsive control law synchronizes all followers with the leader despite deceptive attacks and switching topologies,maintaining robust coordination through nonlinear corrective mechanisms.To validate the approach,simulations are conducted on systems of five and seventeen vehicles in both leaderless and leader—follower configurations.The results demonstrate that the proposed framework achieves rapid consensus,strong robustness,and high resistance to deception attacks,offering a secure and scalable model-based control solution for modern vehicular communication networks.
基金supported by the Liaoning Revitalization Talents Program(XLYC2203148)
文摘Dear Editor,This letter proposes a dynamic switching soft slicing strategy for industrial mixed traffic in 5G networks. Considering two types of traffic, periodic delay-sensitive (PDS) traffic and sporadic delay-tolerant (SDT) traffic, we design a dynamic switching strategy based on a traffic-Qo S-aware soft slicing (TQASS) scheme and a resource-efficiency-aware soft slicing (REASS) scheme.
基金supported by NSF China(No.61960206002,62020106005,42050105,62061146002)Shanghai Pilot Program for Basic Research–Shanghai Jiao Tong University.
文摘Friendship paradox states that individuals are likely to have fewer friends than their friends do,on average.Despite of its wide existence and appealing applications in real social networks,the mathematical understanding of friendship paradox is very limited.Only few works provide theoretical evidence of single-step and multi-step friendship paradoxes,given that the neighbors of interest are onehop and multi-hop away from the target node.However,they consider non-evolving networks,as opposed to the topology of real social networks that are constantly growing over time.We are thus motivated to present a first look into friendship paradox in evolving networks,where newly added nodes preferentially attach themselves to those with higher degrees.Our analytical verification of both single-step and multistep friendship paradoxes in evolving networks,along with comparison to the non-evolving counterparts,discloses that“friendship paradox is even more paradoxical in evolving networks”,primarily from three aspects:1)we demonstrate a strengthened effect of single-step friendship paradox in evolving networks,with a larger probability(more than 0.8)of a random node’s neighbors having higher average degree than the random node itself;2)we unravel higher effectiveness of multi-step friendship paradox in seeking for influential nodes in evolving networks,as the rate of reaching the max degree node can be improved by a factor of at least Θ(t^(2/3))with t being the network size;3)we empirically verify our findings through both synthetic and real datasets,which suggest high agreements of results and consolidate the reasonability of evolving model for real social networks.
