| Presently the studies on complex networks have been penetrated into the subjects ofmathematics, physics, computer, biological sciences and so on, which involves the knowl-edge of nonlinear dynamics, control theory, graph theory. Network modeling is a subjectof the earliest studies of complex networks, focusing on the topological and dynamicalproperties of the considered networks. Compared with random networks, deterministicnetworks have an advantage with analytically obtaining the topological and dynamicalproperties, which could verify some results obtained from random networks. This disser-tation mainly calculates the Laplacian spectrum of some deterministic networks, obtainsthe scalings of coherence with network size, and compares the scaling with other studiednetworks. In details, the main contents of this dissertation are organized as follows:In Chapter I, we give the research background and the current situation of the com-plex network, then we also give the research background and the significance of the Lapla-cian spectrum of the network and the network coherence.Chapter II calculates the Laplacian spectrum of a3-Prism network, and obtains theanalytical solutions of the number of spanning trees and mean first-passage time.In Chapter III, we study the network coherence and calculate the scalings of first andsecond order coherence with network size N. The scalings are ln N and N, which aresmaller than some studied tree networks, which means that the coherence of our networksis not relevant to fractal dimension.In Chapter IV, we investigate the network coherence in a network with infinite fractaldimension and select Web network to study this problem. We then obtain the scalings offirst and second order coherence with network size N. The results show that the scalings inthe Web network are not related to the fractal dimension and larger than those performedon some studied networks.Chapter V summarizes the conclusions and gives further studies in the future. |
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