Study On Network Structure Measurement And Co-Evolution In Propagation Dynamics

Each complex network(class of complex networks)presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network.Therefore,the analysis,discrimination of complex networks and the dynamical behaviours on networks rely on the use of measurements that express the most relevant topological features.In this dissertation,the impact of network structure measurements(i.e.,degree and clustering coefficient)on the dynamic process is stidied under several different complex network dynamics scenarios(i.e.,cascading failure,virus propagation and influence node discovery).A method for quickly identifying high-influence nodes,a new cascade failure model and a virus propagation model considering clustering are proposed.Besides,the dynamic evolution of the network structure and the dynamics of the network are studied,based on which the spreading controlling strategies are designed.The Markov chain method and the dynamic mean-field equation are used to establish an adaptive weighted network model.The reliability(spreading threshold,speed and scale)of the adaptive weighted network model is analyzed,and the spreading control strategies for dynamical networks are proposed.The main contributions of the dissertation are as follows:1.Considering the network scale,the uncertainty of topology and the timeliness of dynamic behavior in real networks,a method for quickly identifying high-influence nodes based on node’s degree is proposed.Instead of ordering the influence of all nodes in the network,our method pays more attention on the finding of small fraction of high-influence nodes quickly in the network,and based on which,the important nodes can be further handled.The comparison between the results of our method and the results obtained by 4 classic node’s influence ranking method shows that our method can quickly and efficiently find high-impact nodes in the network.In addition,it is verified through the propagation process that the target nodes found by our method have a very positive impact on the propagation process in the network.2.A new cascade failure model is proposed to analyze the robustness of the network under node failure,and a load redistribution strategy based on local real-time information is designed.The theoretical analysis of the impact of load redistribution strategy on network robustness is carried out,and the relationship between network robustness and redistribution strategy parameters in different situations is discussed.The analysis shows that when the initial load distribution and load redistribution strategy of the network are the same and linear with the degree of the node,the network shows better robustness under cascading failure.Furthermore,it is effective to allocate the node’s load according to the degree to improve the network robustness in the lack of the initial load information.The numerical simulation results in artificial network and real-life network confirm the correctness of the theoretical analysis of the robustness threshold and load redistribution strategy.3.A SIS epidemic spreading model consider the clustering characteristics of the networks is proposed,and the influence of clustering coefficients on epidemic spreading in studied.Our results show that the clustering characteristics of different networks have different inhibitory effects on epidemic spreading.In the homogeneous networks,when the probability of infection is small,the final epidemic size decreases as the clustering coefficient increases.However,as the probability of infection increases,the clustering characteristics gradually lose their inhibitory effect on epidemics.More interestingly,in the heterogenous networks and the null models based on the real networks,the clustering coefficient has almost no inhibitory effect on epidemics,that is,the network clustering can hardly affect the propagation threshold and the final propagation scale.4.A new mean-field model to analyze the resistance of adaptive weighted networks against cascading failures,such as DDoS attack and computer virus is proposed.A new set of differential equations are formulated to model the continuous-time Markov chain process of the rewiring of weighted links in adaptive weighted networks.The largest eigenvalue of the Jacobian matrix of the linearization is the key to the study of the network reliability,but not readily achievable.The eigenvalues of the the Jacobian matrix are evaluated by using determinant transformations and spectral analysis,and finally unveil the range of the largest eigenvalue of the Jacobian matrix.The upper and lower bounds of the range provide the sufficient conditions for the inhibition and proliferation of virus or cascading failures in adaptive weighted networks.Two case studies verify the conditions,with exponentially and log-normally distributed link weights.By exploiting Order Statistics and Taylor expansion,we reveal that the condition of proliferation of virus or cascading failures is inversely proportional to both the network degree and average link weight.5.Considering the diversity of interpersonal relationships and the ability of network topology to dynamically adapt to the state of nodes,a new weighted adaptive heterogeneous network is proposed based on SIS propagation model.The epidemic spreading process in weighted adaptive heterogeneous networks is studied,and the influence of network structure on epidemiology is discussed.In addition,based on the individual behavior in the network,the rewiring strategies on the inhibition of epidemics are proposed.The analysis results show that the greater the dispersion of the initial network weights,the slower the propagation in the network.The adaptive link rewriring process can effectively suppress the spread of epidemics.Our simulation results also show that the proposed rewiring stategies based on the real-time edge weights can effectively inhibit the spread of epidemics.