Influential Dimension In Complex Networks: Model And Instances

Most real world networks have their background spaces, for instance, human relation networks are constrained by geographic factors, internet and power networks are always embedded on the surface of earth. Thus, its reasonable to add geographical influences into the mechanism of growing model. In a model with adaption of geographical influences, a node is most likely connected to some nearest nods for its ability to know the state of the whole network is very limited. However, real world networks suffers influences not only from geographic influences, but also from others. For instance, train, power, and bus networks can be influenced by local economics;human relationship networks can be influenced by personal hobbies, family environment, education, etc. These influences urge us to adopt new weights on network models. We noticed that real world networks are limited in network scale, and most of its newly generated nodes have very limited information of the whole states of the network. Therefor, it's reasonable under physical intuition while we choose a nearest growing model without the consideration of boundary condition. Substituted by different dimensions, outer influences are considered thus nearest growing model in influential spaces were proposed.Beside studying its properties of this network model, we studied some real world networks, and compared their characteristics while positive fits are obtained. We obtain that this kind of mechanism of growing model means a lot to the definition of dimension on complex networks and dimension plays a important part in dynamics of complex networks. Can we imply that model of general networks undergo some macro characteristic influences corresponding to the geometrical definition of networks? If so, problem arises in the definition of dimension in general networks.In this thesis, we begin with basic concepts of graph theory and complex networks, and proposes our influential nearest growing model without boundary condition, then comes with the comparasion of this model and studied real world networks. Finally, we discuss the dynamics of networks.