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Random walk-based link prediction algorithms have achieved desirable results for complex network mining, but in these algorithms, the transition probability of particles usually only considers node degrees, resulting in particles being able to randomly select adjacent nodes for random walks in an equal probability manner, to solve this problem, the asymmetric influence-based superposed random walk link prediction algorithm is proposed in this paper. This algorithm encourages particles to choose the next node at each step of the random walk process based on the asymmetric influence between nodes. To this end, we fully consider the topological information around each node and propose the asymmetric influence between nodes. Then, an adjustable parameter is applied to normalize the degree of nodes and the asymmetric influence between nodes into transition probability. Based on this, the proposed new transition probability is applied to superposed random walk process to measure the similarity between all nodes in the network. Empirical experiments are conducted on 16 real-world network datasets such as social network, ecology network, and animal network. The experimental results show that the proposed algorithm has high prediction accuracy in most network, compared with 10 benchmark indices.

In the current landscape, the Internet of Things (IoT) finds its utility across diverse sectors, including finance, healthcare, and beyond. However, security emerges as the principal obstacle impeding the advancement of IoT. Given the intricate nature of IoT cybersecurity, traditional security protocols fall short when addressing the unique challenges within the IoT domain. Security strategies anchored in the cybersecurity knowledge graph present a robust solution to safeguard IoT ecosystems. The foundation of these strategies lies in the intricate networks of the cybersecurity knowledge graph, with Named Entity Recognition (NER) serving as a crucial initial step in its implementation. Conventional cybersecurity entity recognition approaches IoT grapple with the complexity of cybersecurity entities, characterized by their sophisticated structures and vague meanings. Additionally, these traditional models are inadequate at discerning all the interrelations between cybersecurity entities, rendering their direct application in IoT security impractical. This paper introduces an innovative Cybersecurity Entity Recognition Model, referred to as CERM, designed to pinpoint cybersecurity entities within IoT. CERM employs a hierarchical attention mechanism that proficiently maps the interdependencies among cybersecurity entities. Leveraging these mapped dependencies, CERM precisely identifies IoT cybersecurity entities. Comparative evaluation experiments illustrate CERM’s superior performance over the existing entity recognition models, marking a significant advancement in the field of IoT security.

Despite extensive efforts to the continuous-time Markov process of the susceptible–infected–susceptible (SIS) model, there remains a dearth of efficient methods for numerically simulating the continuous-time spreading paths in complex networks using discrete-time simulations. In typical discrete-time approaches to the SIS model, time is discretized into small uniform intervals, and synchronous updating schemes are commonly employed to update the states of nodes. However, in this study, we demonstrate that the synchronous updating scheme introduces undesired noise, such as period-doubling and chaotic behaviors, into the spreading paths, diverging from the continuous-time SIS model. Additionally, we observe that the classical synchronous discrete-time scheme underestimates the spreading ability as compared to the corresponding continuous-time SIS model, a discrepancy that is dependent on the length of the time intervals. Leveraging the Taylor formalism, we propose a novel synchronous discrete-time updating method that addresses these issues associated with the classical synchronous discrete-time scheme. Importantly, our proposed method achieves high accuracy regardless of the length of the time intervals, which can be further exploited to enhance simulation speed. Experiments in both artificial and real networks show that our method approximates the continuous-time spreading paths better and costs less computing time than the classical discrete-time synchronous method.

Although much attention has been focused on traffic-driven epidemic spreading on complex networks, the vast majority of theoretical approaches assumes an identical infection rate for all nodes. This paper investigates the effect of heterogenous infection rates on epidemic spreading, in which the infection rate obeys Binomial distribution. Mean-field approximation and continuous-time Markov chain are adopted to establish the control equation for the model. Results show that heterogeneous infection rates can suppress or promote the epidemic spreading. By adjusting the parameters of infection heterogeneity or the proportion of different nodes, the scope and the threshold of epidemic spreading can be controlled. Simulations on Erdös–Rényi random networks and Barabási–Albert scale-free networks prove the accuracy of theoretical predictions.

Identifying important nodes is a long-standing topic of discussion in the field of complex networks. Most current methods focus on either local or global attributes of nodes, or a simple combination of both. However, in real-world networks, the influence of local and global attributes on nodes varies significantly. Therefore, determining how to accurately assess the weights of different attributes for different networks to enhance the identification of important nodes remains an urgent challenge. In this paper, we propose a multi-attribute decision fusion method named SK-E. This method constructs both local and global metrics for diverse networks and employs an improved Electre approach to fuse these metrics. By determining the optimal weight between local and global metrics, SK-E effectively identifies important nodes in network datasets with varying topological structures. Evaluated using four indices (SIR epidemic model, independent cascade model, Kendall coefficient and constraint efficiency) across nine real networks, the proposed method exhibits superior accuracy compared to existing methods.

As a low-carbon transport mode, the railway has a significant influence on transport CO₂ emissions. This paper abstracts and quantifies the influence from a new perspective to explore the influence of the railway industry on transport CO₂ emissions. Considering various influencing factors systematically, we establish the transport CO₂ emissions correlation (TCEC) network based on the theory of complex networks. The superimposed influence diffusion (SID) model proposed in this paper can predict the future trend of the transport CO₂ emissions through network evolution, which is different from traditional methods. The railway-related scenarios are designed to analyze the influence spread and the possibility of Beijing peaking the transport CO₂ emissions before 2035. The research results show that the transport CO₂ emissions reach a peak and then slowly decrease under four scenarios, while under other scenarios, the transport CO₂ emissions keep growing unable to achieve a peak. The proposed methods can be extended to other areas, and the research findings have certain reference for making policies.

With the increasing trend of global population aging, traditional risk assessment methods often overlook the nonlinear interactions and dynamic feedback mechanisms between various elements in the system, making it difficult to capture the complex process of risk evolution. This study identified and characterized the complex relationships between participants in the pension financial system through complex network analysis, including fund flows, policy impacts, market fluctuations, and other dimensions. Then, partial differential equations (PDEs) were introduced as the core modeling tool, and a pension financial system based on partial differential equations (PFS-PDE) risk dynamic evolution model was established by combining PDEs. The PFS-PDE model achieved a relatively high intersection over union (IOU) value after fewer training iterations (about 30) and remained relatively stable thereafter, indicating that the model has a fast convergence speed. The PFS-PDE model has relatively low mean square error (MSE) values and a relatively small fluctuation range under most training iterations, which can be considered as a relatively better performance. Compared with other models, the PFS-PDE model has a smaller range of MSE value fluctuations, indicating that the model has high stability during the training process.

Neuromodulation plays a vital role in the prevention and treatment of neurological and psychiatric disorders. Neuromodulation’s feasibility is a long-standing issue because it provides the necessity for neuromodulation to realize the desired purpose. A controllability analysis of neural dynamics is necessary to ensure neuromodulation’s feasibility. Here, we present such a theoretical method by using the concept of controllability from the control theory that neuromodulation’s feasibility can be studied smoothly. Firstly, networks of multiple coupled neural populations with different topologies are established to mathematically model complicated neural dynamics. Secondly, an analytical method composed of a linearization method, the Kalman controllable rank condition and a controllability index is applied to analyze the controllability of the established network models. Finally, the relationship between network dynamics or topological characteristic parameters and controllability is studied by using the analytical method. The proposed method provides a new idea for the study of neuromodulation’s feasibility, and the results are expected to guide us to better modulate neurodynamics by optimizing network dynamics and network topology.

Speech sounds of the languages all over the world show remarkable patterns of co-occurrence. In this work, we attempt to automatically capture the patterns of co-occurrence of the consonants across languages and at the same time figure out the nature of the force leading to the emergence of such patterns. For this purpose we define a weighted network where the consonants are the nodes and an edge between two nodes (read consonants) signify their co-occurrence likelihood over the consonant inventories. Through this network we identify communities of consonants that essentially reflect their patterns of co-occurrence across languages. We test the goodness of the communities and observe that the constituent consonants frequently occur in such groups in real languages also. Interestingly, the consonants forming these communities reflect strong correlations in terms of their features, which indicate that the principle of feature economy acts as a driving force towards community formation. In order to measure the strength of this force we propose a theoretical information definition of feature economy and show that indeed the feature economy exhibited by the consonant communities are substantially better than that of those where the consonant inventories had evolved just by chance.

In this paper, we present the dynamics of disaster spreading from key nodes in complex networks. The key nodes have maximum and minimum out-degree nodes, which show important in spreading disaster. This paper considers directed Erdös–Rényi, scale-free and small-world networks. Using the model considering the common characteristics of infrastructure and lifeline networks, i.e., self-healing function and disaster spreading mechanism, we carry out simulations for the effects of the recovery time parameter and the time delay on the recovery rate and the number of damaged nodes. Simulation results show some typical disaster spreading characteristics, e.g., a non-equilibrium phase transition in the parameter space, disturbance from the maximum out-degree nodes resulting in more damaged effect, etc.

In this paper, we study a model of opinion spreading and consensus formation on a square lattice. Given a two-dimensional square lattice with periodic boundary condition, a total fraction p of the sites are occupied by agents. We take into account the drift ability of the focal agents whose opinions' difference is too large. The dynamics of the model is governed by the following two rules. At each time step, the agents (or individuals) can exchange their opinions with those of their neighbors if the difference between them is smaller than the "bounded confidence" ∊; Otherwise, one can move to a vacancy location if permitted (i.e., there are any empty sites existing among the focal agent's neighborhood). The distribution of opinions over the population evolves toward either a consensus state that all individuals share the same opinion or polarization and fragmentation states where two or more opinions can coexist. The statistical properties of this final state vary considerably as the parameters p and ∊ change. It is shown that, when dispersal abilities of the individuals are considered, the bounded confidence which is required to attain consensus can be remarkably decreased.

Recent advances in complex network research have stimulated increasing interests in understanding the relationship between the topology and dynamics of complex networks. Based on the theory of complex networks and computer simulation, we analyze the robustness to time-delay in linear consensus problem with different network topologies, such as global coupled network, star network, nearest-neighbor coupled network, small-world network, and scale-free network. It is found that global coupled network, star network, and scale-free network are vulnerable to time-delay, while nearest-neighbor coupled network and small-world network are robust to time-delay. And it is found that the maximum node degree of the network is a good predictor for time-delay robustness. And it is found that the robustness to time-delay can be improved significantly by a decoupling process to a small part of edges in scale-free network.

We further study the competition among loner, cooperative and defective strategies by considering an evolutionary prisoner's dilemma (PD) game with some troublemakers in the random network by means of Monte Carlo simulations. It can be observed that the frequency of cooperators (f_c) decreases with increasing of loners' (e) and defectors' payoffs (b). In particular, f_c has a sharp decline when the loners' payoffs approximate 1.0. In addition, we find that introduction of troublemaker strategies prevents the uniform defection in the spatial evolutionary PD games for large b values and small e values. In practice, it also prevents cooperative strategies and defective strategies from vanishing for large e values.

In this paper, a growing network model with aging mechanism is investigated. Each new node of the network gets attached to the ith existing node with the probability , where k_i is the degree of the ith node and τ_i is its age at time t. β denotes attraction factor and α represents aging intensity. It is found that the network shows scaling behaviors such as scale-free and exponential distribution of degree. Moreover, the phase diagram in the β - α plane is observed, in which there are three regions plotted by two boundaries.

In the cellular automata traffic flow model, the traffic state can be represented by the discrete speed value of vehicles, thus the traffic flow can be deemed as a discrete dynamical system. In the evolution process of traffic flow, complex networks are constructed by representing the traffic state as node and the evolution relationship in timescale as link. The emerging times of link is defined as its weight, then the node strength is equal to the emerging times of the corresponding traffic state. As a result, a weighted network is obtained. The dynamics of stop-and-go traffic are studied by investigating the statistical properties of the network. Simulation results show that scale-free behavior commonly exists in the evolution process of stop-and-go traffic. The degree distribution, node strength distribution and link weight distribution have the power law form. The node with high degree also has large strength. The structure of the network is not influenced by the randomization probability and density as long as the stop-and-go traffic is reproduced.

A new model for describing the disaster system including instantaneous and continuous action synchronously has been developed. The model is composed of three primary parts, that is, the impact from its causative disaster events, stochastic noise of disaster node and self-healing function, and every part is modeled concretely in terms of their characteristics in practice. Some key parameters, namely link appearance probability, retardation coefficient, ultimate repair capacity of government, dynamical modes considering different disaster evolving chains, and the positions of link with the specific performance in disaster network system are involved. Combined with a case study, the proposed model is applied to a certain disaster evolution system, and the influence law of different parameters on disaster evolution process, in disaster networks with instantaneous-action and/or continuous-action, is presented and compared. The results indicate that the destructive impact in the networks by link in continuous action is far greater an order of magnitude than that in instantaneous action. If a link in continuous action emerges in the disaster network system, properties of the causative event for the link, link appearance probability and its position in the network all have a notable influence to the severity of the disaster network. In addition, some peculiar phenomena are also commendably observed in the disaster evolution process based on the model, such as the multipeaks emerging in the destroyed rate number curve for some crisis nodes caused by their various inducing paths together with the relevant retardation coefficients, the existence of the critical value for ultimate repair capacity to recover the disaster node, and so on.

In this brief report, we investigate the synchronizability of the complex network. In order to optimize the synchronizability, we propose a method by introducing a weight matrix, which makes the synchronized states stable for the widest range of the overall coupling strength. We give a proof in mathematics and gain the exact form of the weight matrix, which is equal to Lβ. Matrix L is the one that describes the optimal network and matrix β is constructed by the eigenvalues and eigenvectors of the usual Laplacian matrix. This result may provide us insight into the synchronization of complex network more deeply.

For the complex networks, including scale-free, small-world, local-world and random networks, the global quantitative evaluation of attack-induced cascade is investigated in this paper by introducing the risk assessment, which integrates the probability of occurrence with the damage size of attacks on nodes. It is discovered by simulations, among the several kinds of networks, that the small-world network has the largest risk assessment of attack-induced cascade; the risk assessment of three other networks are all very low and the most protection against attack should be given to the small-world network accordingly. Furthermore, the percentage of the most fragile nodes in the scale-free network is very low, compared with that in the small-world network.

This paper investigates the exponential synchronization of complex network with non-delayed and delayed coupling. A periodically intermittent controller is designed to synchronize the network onto a given orbit. Based on Lyapunov function and differential inequality method, the criteria for exponential synchronization are derived. Numerical simulation is presented to verify the effectiveness of the derived results.

We systematically carried out oil–gas–water three-phase flow experiments for measuring the time series of flow signals. We first investigate flow pattern behaviors from the energy and frequency point of view and find that different flow patterns exhibit different flow behaviors. In order to quantitatively characterize dynamic behaviors underlying different oil–gas–water three-phase flow patterns, we infer and analyze visibility graphs (complex networks) from signals measured under different flow conditions. The results indicate that the combination parameters of network degree are sensitive to the transition among different flow patterns, which can be used to distinguish different flow patterns and quantitatively characterize nonlinear dynamics of the three-phase flow. In this regard, visibility graph can be a useful tool for characterizing the nonlinear dynamic behaviors underlying different oil–gas–water three-phase flow patterns.