Coherence And Its Optimization In Noisy Scale-free Networks

With the rapid development of science and technology,the daily life and productive activities of human society are more and more rely on the safe and efficient operation of various complex network systems,such as Internet,mobile communication network,infrastructure network and public transportation network.Many networks are proved to obey scale-free power law distribution,and their topologies are robust and fragile.How to describe the characteristics of scale-free networks from other dynamical perspectives has been a hot topic in the field of networks.This dissertation takes the coherence of linear system with noise as the research object and uses the Laplacian spectrum of the network to describe it.We focus on the robustness of scale-free network coherence,explore topological structures which affect coherence,propose a new index names as leader centrality based on coherence,and further analyze the issue of network coherence optimization.The specific work is as follows:1.We study the robustness of scale-free networks coherence.Firstly,we propose a scale-free model with expected average degree and analyze the relations between the three coherence indices and the average degree.It is shown that the coherence with higher average degree is better with the same network size,and coherence has a little change with the network size for constant average degree.In addition,we discuss the robustness of network coherence under random nodal failures and target attacks.In target attacks,the nodes and edges are removed by ranking nodes in a descending order based on the degree,closeness and eigenvector centrality.The numerical results reveal that target attacks have a larger impact on the coherence than random nodal failures.Meanwhile,in the leaderless dynamics,the network coherence becomes worse under the attacks of degree and closeness centrality,while in the leader-follower dynamics,the removed leaders have a greater effect on the coherence.2.We construct a combinatorial optimization model with the network coherence as the optimization objective and the fixed degree distribution and connectivity as constraint condition.In view of the complexity of the problem,we use simulated annealing algorithm and tabu search algorithm to optimize and reconstruct the initial network.The results show that the two algorithms can improve the coherence of the network to some extent,but the latter has a better optimization effect.3.We propose a new centrality index names as leader centrality,which bases on coherence and simulate the spreading process of Susceptible-Infected-Recovered model and independent cascade model in scale-free model networks and real networks.It is proven that compared to other centrality indices,leader centrality is more effective to identify the influential spreaders in the network,which is of great guiding significance to the advertising,rumor spreading and et al.