Immunization for scale-free networks by random walker

Based on the random walk and the intentional random walk, we propose two types of immunization strategies which require only local connectivity information. On several typical scale-free networks, we demonstrate that these strategies can lead to the eradication of the epidemic by immunizing a small fraction of the nodes in the networks. Particularly, the immunization strategy based on the intentional random walk is extremely efficient for the assortatively mixed networks.

Epidemic spreading in scale-free networks including the effect of individual vigilance

In this paper, we study the epidemic spreading in scale-flee networks and propose a new susceptible-infected- recovered （SIR） model that includes the effect of individual vigilance. In our model, the effective spreading rate is dynamically adjusted with the time evolution at the vigilance period. Using the mean-field theory, an analytical result is derived. It shows that individual vigilance has no effect on the epidemic threshold. The numerical simulations agree well with the analytical result. Purthermore, we investigate the effect of individual vigilance on the epidemic spreading speed. It is shown that individual vigilance can slow the epidemic spreading speed effectively and delay the arrival of peak epidemic infection.

Cascading failure in the wireless sensor scale-free networks

In the practical wireless sensor networks （WSNs）, the cascading failure caused by a failure node has serious impact on the network performance. In this paper, we deeply research the cascading failure of scale-free topology in WSNs. Firstly, a cascading failure model for scale-free topology in WSNs is studied. Through analyzing the influence of the node load on cascading failure, the critical load triggering large-scale cascading failure is obtained. Then based on the critical load, a control method for cascading failure is presented. In addition, the simulation experiments are performed to validate the effectiveness of the control method. The results show that the control method can effectively prevent cascading failure.

Malicious Code Modeling and Analysis in Weighted Scale-Free Networks

We study the detailed malicious code propagating process in scale-free networks with link weights that denotes traffic between two nodes. It is found that the propagating velocity reaches a peak rapidly then decays in a power-law form, which is different from the well-known result in unweighted network case. Simulation results show that the nodes with larger strength are preferential to be infected, but the hierarchical dynamics are not clearly found. The simulation results also show that larger dispersion of weight of networks leads to slower propagating, which indicates that malicious code propagates more quickly in unweighted scale-free networks than in weighted scale-free networks under the same condition. These results show that not only the topology of networks but also the link weights affect the malicious propagating process.

Epidemic spreading on a scale-free network with awareness

This paper presents a modified susceptible-infected-recovered（SIR） model with the effects of awareness and vaccination to study the epidemic spreading on scale-free networks based on the mean-field theory.In this model,when susceptible individuals receive awareness from their infected neighbor nodes,they will take vaccination measures.The theoretical analysis and the numerical simulations show that the existence of awareness and vaccination can significantly improve the epidemic threshold and reduce the risk of virus outbreaks.In addition,regardless of the existence of vaccination,the awareness can increase the spreading threshold and slow the spreading speed effectively.For a given awareness and a certain spreading rate,the total number of infections reduces with the increasing vaccination rate.

Degree distribution and robustness of cooperative communication network with scale-free model

With the requirements of users enhanced for wireless communication, the cooperative communication will become a development trend in future. In this paper, a model based on complex networks with both preferential attachment is researched to solve an actual network CCN （Cooperative Communication Network）. Firstly, the evolution of CCN is given by four steps with different probabilities. At the same time, the rate equations of nodes degree are presented to analyze the evolution of CCN. Secondly, the degree distribution is analyzed by calculating the rate equation and numerical simulation. Finally, the robustness of CCN is studied by numerical simulation with random attack and intentional attack to analyze the effects of degree distribution and average path length. The results of this paper are more significant for building CCN to programme the resource of communication.

Improving Dendritic Neuron Model With Dynamic Scale-Free Network-Based Differential Evolution

Some recent research reports that a dendritic neuron model(DNM)can achieve better performance than traditional artificial neuron networks(ANNs)on classification,prediction,and other problems when its parameters are well-tuned by a learning algorithm.However,the back-propagation algorithm(BP),as a mostly used learning algorithm,intrinsically suffers from defects of slow convergence and easily dropping into local minima.Therefore,more and more research adopts non-BP learning algorithms to train ANNs.In this paper,a dynamic scale-free network-based differential evolution(DSNDE)is developed by considering the demands of convergent speed and the ability to jump out of local minima.The performance of a DSNDE trained DNM is tested on 14 benchmark datasets and a photovoltaic power forecasting problem.Nine meta-heuristic algorithms are applied into comparison,including the champion of the 2017 IEEE Congress on Evolutionary Computation(CEC2017)benchmark competition effective butterfly optimizer with covariance matrix adapted retreat phase(EBOwithCMAR).The experimental results reveal that DSNDE achieves better performance than its peers.

Enhancement of scale-free network attack tolerance

Despite the large size of most communication and transportation systems, there are short paths between nodes in these networks which guarantee the efficient information, data and passenger delivery; furthermore these networks have a surprising tolerance under random errors thanks to their inherent scale-free topology. However, their scale-free topology also makes them fragile under intentional attacks, leaving us a challenge on how to improve the network robustness against intentional attacks without losing their strong tolerance under random errors and high message and passenger delivering capacity. Here We propose two methods （SL method and SH method） to enhance scale-free network＇s tolerance under attack in different conditions.

Adaptive local routing strategy on a scale-free network

Due to the heterogeneity of the structure on a scale-free network, making the betweennesses of all nodes become homogeneous by reassigning the weights of nodes or edges is very difficult. In order to take advantage of the important effect of high degree nodes on the shortest path communication and preferentially deliver packets by them to increase the probability to destination, an adaptive local routing strategy on a scale-free network is proposed, in which the node adjusts the forwarding probability with the dynamical traffic load （packet queue length） and the degree distribution of neighbouring nodes. The critical queue length of a node is set to be proportional to its degree, and the node with high degree has a larger critical queue length to store and forward more packets. When the queue length of a high degree node is shorter than its critical queue length, it has a higher probability to forward packets. After higher degree nodes are saturated （whose queue lengths are longer than their critical queue lengths）, more packets will be delivered by the lower degree nodes around them. The adaptive local routing strategy increases the probability of a packet finding its destination quickly, and improves the transmission capacity on the scale-free network by reducing routing hops. The simulation results show that the transmission capacity of the adaptive local routing strategy is larger than that of three previous local routing strategies.

Effects of channel noise on synchronization transitions in delayed scale-free network of stochastic Hodgkin–Huxley neurons

We numerically study the effect of the channel noise on the spiking synchronization of a scale-free Hodgkin-Huxley neuron network with time delays. It is found that the time delay can induce synchronization transitions at an intermediate and proper channel noise intensity, and the synchronization transitions become strongest when the channel noise intensity is optimal. The neurons can also exhibit synchronization transitions as the channel noise intensity is varied, and this phenomenon is enhanced at around the time delays that can induce the synchronization transitions. It is also found that the synchronization transitions induced by the channel noise are dependent on the coupling strength and the network average degree, and there is an optimal coupling strength or network average degree with which the synchronization transitions become strongest. These results show that by inducing synchronization transitions, the channel noise has a big regulation effect on the synchronization of the neuronal network. These findings could find potential implications for the information transmission in neural systems.

Generalized minimum information path routing strategy on scale-free networks

This paper presents a new routing strategy by introducing a tunable parameter into the minimum information path routing strategy we proposed previously. It is found that network transmission capacity can be considerably enhanced by adjusting the parameter with various allocations of node capability for packet delivery. Moreover, the proposed routing strategy provides a traffic load distribution which can better match the allocation of node capability than that of traditional efficient routing strategies, leading to a network with improved transmission performance. This routing strategy, without deviating from the shortest-path routing strategy in the length of paths too much, produces improved performance indexes such as critical generating rate, average length of paths and average search information.

Mobile user forecast and power-law acceleration invariance of scale-free networks

This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well.

A Novel Neighbor-Preferential Growth Scale-Free Network Model and its Properties

In this paper, we propose a novel neighbor-preferential growth (NPG) network model. Theoretical analysis and numerical simulations indicate the new model can reproduce not only a scale-free degree distribution and its power exponent is related to the edge-adding number m, but also a small-world effect which has large clustering coefficient and small average path length. Interestingly, the clustering coefficient of the model is close to that of globally coupled network, and the average path length is close to that of star coupled network. Meanwhile, the synchronizability of the NPG model is much stronger than that of BA scale-free network, even stronger than that of synchronization-optimal growth network.

The Analysis of an SIRS Epidemic Model with Discrete Delay on Scale-Free Network

A new epidemic SIRS model with discrete delay on scale-free network is presented. We give the formula of the basic reproductive number for the model and prove that the disease dies out when the basic reproductive number is less than unity, while the disease is uniformly persistent when the basic reproductive number is more than unity. Numerical simulations are given to demonstrate the main results.

Robustness measurement of scale-free networks based on motif entropy

As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structural integrity, functional integrity and dynamics of the networks. In order to overcome the shortcomings in the existing work on the robustness of complex networks, only nodes or edges are considered, while the defects of high-order structure in the network are ignored.From the perspective of network motif, we propose an entropy of node degree distribution based on motif to measure the robustness of scale-free networks under random attacks. The effectiveness and superiority of our method are verified and analyzed in the BA scale-free networks.

Modelling the spread of sexually transmitted diseases on scale-free networks

In this paper a new model for the spread of sexually transmitted diseases （STDs） is presented. The dynamic behaviors of the model on a heterogenons scale-free （SF） network are considered, where the absence of a threshold on the SF network is demonstrated, and the stability of the disease-free equilibrium is obtained. Three immunization strategies, uniform immunization, proportional immunization and targeted immunization, are applied in this model. Analytical and simulated results are given to show that the proportional immunization strategy in the model is effective on SF networks.

Convergence speed of consensus problems over undirected scale-free networks

Scale-free networks and consensus behaviour among multiple agents have both attracted much attention. To investigate the consensus speed over scale-free networks is the major topic of the present work. A novel method is developed to construct scale-free networks due to their remarkable power-law degree distributions, while preserving the diversity of network topologies. The time cost or iterations for networks to reach a certain level of consensus is discussed, considering the influence from power-law parameters. They are both demonstrated to be reversed power-law functions of the algebraic connectivity, which is viewed as a measurement on convergence speed of the consensus behaviour. The attempts of tuning power-law parameters may speed up the consensus procedure, but it could also make the network less robust over time delay at the same time. Large scale of simulations are supportive to the conclusions.

Evolution of donations on scale-free networks during a COVID-19 breakout

Having a large number of timely donations during the early stages of a COVID-19 breakout would normally be considered rare. Donation is a special public goods game with zero yield for donors, and it has the characteristics of the prisoners’ dilemma. This paper discusses why timely donations in the early stages of COVID-19 occurred. Based on the idea that donation is a strategy adopted by players during interconnection on account of their understanding of the environment, donation-related populations are placed on social networks and the inter-correlation structures in the population are described by scale-free networks. Players in donation-related populations are of four types: donors, illegal beneficiaries,legal beneficiaries, and inactive people. We model the evolutionary game of donation on a scale-free network. Donors,illegal beneficiaries and inactive people learn and update strategies under the Fermi update rule, whereas the conversion between legal beneficiaries and the other three types is determined by the environment surrounding the players. We study the evolution of cooperative action when the agglomeration coefficient, the parameters of the utility function, the noise intensity, the utility coefficient, the donation coefficient and the initial states of the population on the scale-free network change. For population sizes of 50, 100, 150, and 200, we give the utility functions and the agglomeration coefficients for promoting cooperation and study the corresponding steady states and structural characteristics of the population. We identify the best ranges of the noise intensity K, the donation coefficient α and the utility coefficient β for promoting cooperation at different population sizes. Furthermore, with the increase of the population size, the donor traps are found.At the same time, it is discovered that the initial states of the population have a great impact on the steady states;thus the upper and lower triangle phenomena are proposed. We also find that the population size itself is also an important factor for promoting donation, pointing out the direction of efforts to further promote donation and achieve better social homeostasis under the donation model.

Improving consensual performance of multi-agent systems in weighted scale-free networks

This paper studies consensus problems in weighted scale-free networks of asymmetrically coupled dynamical units, where the asymmetry in a given link is deter：mined by the relative degree of the involved nodes. It shows that the asymmetry of interactions has a great effect on the consensus. Especially, when the interactions are dominant from higher- to lower-degree nodes, both the convergence speed and the robustness to communication delay are enhanced.

Study on the phase transition of the fractal scale-free networks

Based on the Ising spin, the phase transition on fractal scale-free networks with tree-like skeletons is studied, where the loops are generated by local links. The degree distribution of the tree-like skeleton satisfies the power-law form P（k）～ k^-δ.It is found that when δ≥3, the renormalized scale-free network will have the same degree distribution as the original network. For a special case of δ = 4.5, a ferromagnetic to paramagnetic transition is found and the critical temperature is determined by the box-covering renormalization method. By keeping the structure of the fractal scale-free network constant, the numerical relationship between the critical temperature and the network size is found, which is the form of power law.