Mutifractality Analysis Of Weighted Koch Networks And Identifying Influential Nodes In Temporal Networks

In this thesis, we concentrate on weighted networks and temporal networks, they are two types of general complex networks. For weighted networks, we focus on the analyses of fractal and multifractal properties of the networks. For temporal networks, we focus on identifying the importance of nodes in the networks.In recent years, weighted networks have been given attention by the fact that they can better able to characterize the structural characteristics of complex systems, but there is few related research work about fractal and multifractal in this kind of networks. In this thesis,inspired by Koch network and Koch island, a new type of weighted Koch network model is proposed as a model framework for the study of weighted networks, then the topological properties and eigenvalue spectrum of the new weighted Koch networks are studied. It is found that the proposed networks are fractal networks and have multifractal behavior.Finally, the methods are applied to study the real world networks, and we show that some real world networks also have similar properties like non-weighted networks, but there is no obvious relation of property between the weighted networks and non-weighted networks.Locating influential nodes in temporal networks has attracted a lot of attention as data driven and diverse applications. Classic works either looked at analysing static network-s or placed too much emphasis on the topological information but rarely highlighted the dynamics. In this thesis, we take account the network dynamics and extend the concept of Dynamic-Sensitive centrality to temporal network. According to the empirical results on three real-world temporal networks and a theoretical temporal network for susceptible-infected-recovered (SIR) models, the temporal Dynamic-Sensitive centrality (TDC) is more accurate than both static versions and temporal versions of degree, closeness and between-ness centrality. As an application, we also use TDC to analyse the impact of time-order on spreading dynamics, we find that both topological structure and dynamics contribute the impact on the spreading influence of nodes, and the impact of time-order on spreading in-fluence will be stronger when spreading rate ? deviated from the epidemic threshold ?c,especially for the temporal scale-free networks.