Different complex systems, are typically large collections of connected elements that influence each other. Some examples are the brain, society, traffic, the financial system, interacting institutions, climate, ecosystems, interacting atoms or molecules and the World Wide Web. Complex systems show non-linear dynamics which means that they may suddenly change behaviour or move to another regime, for example, from a non-synchronous state to a synchronous state. Another characteristic of a complex system is limited predictability. Small changes in initial conditions can lead to very different dynamics over time. The aim of this study is to derive traits on how the dynamical behaviour of a complex system depends on the combined properties of individual elements and the nature of their interactions. Complex systems can be modelled and analysed using graph theory based complex networks, for which the topology of the network plays an important role. These networks consists of nodes which represent single subsystems and edges, which represent interactions between these subsystems. Studies have also shown that changing properties of nodes and edges with time can be used to understand the relationship between the dynamics of the system and its underlying structure. The importance of nodes and edges in structure and dynamics of complex networks can be characterised by certain measures, such as centralities. In order to study the effects of uncertainties in a complex system, a perturbation experiment was performed in the network models such that it is possible to make observations of a change in the model and have some kind of comparison with a real world system. The goal was to estimate the importance of edges using centrality measures and to check the robustness of these edges in both structural and functional networks. Complex dynamical systems consisting of well understood subsystems - the Kuramoto Oscillator. The underlying topology of the system’s interactions is defined using the network models. The properties of the system’s interactions is understood using a network based approach that can help to further comprehend the system’s dynamics.