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- Type of Document: M.Sc. Thesis
- Language: English
- Document No: 46992 (52)
- University: Sharif University of Technology, International Campus, Kish Island
- Department: Science and Engineering
- Advisor(s): Sarbazi Azad, Hamid; Zarei, Mina
- Abstract:
- It has been shown that there is a relationship between the topological and spectral properties of a graph and its dynamics. However, most of the studies have not considered the direction of the links, even though most of the real networks are directed. In this thesis, we study the intrinsic relationship between the graphs’ structures, the spectral characteristics of their associated matrices, and the synchronization implications for different directed random graphs by changing their link directionality. To this end we make use of Kuramoto model for modeling the synchronization dynamics of the network. We show that, in contrast to the results of studies which suggest the λ2/λN as a measure of synchronizability, it is not appropriate for all directed graphs and therefore we introduce an appropriate measure called average Inverse Participation Ratio of the graph. We also show that while recent studies expect strong synchronization in graphs having no or less loops, it is not true for all graphs. In this thesis we state that by balancing the in and out degrees of the nodes in the graph, the distribution of the real part of eigenvalues describes the undirected topology of the graph. We also show that when the graph contains a directed linear flow, it will be more sensitive to the initial frequency distribution of oscillators. We also report some further results obtained from the spectral analysis
- Keywords:
- Spectra ; GRAPH ; Structure ; Synchronisation ; Small World Network ; Directed Network
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