Venetia Voutsa

• The relationship between network structure (structural connectivity, SC) and network representations of dynamics (functional connectivity, FC) is a topic of high scientific interest both for advancing theoretical understanding of complex systems and for its relevance to a wide range of applications. In this thesis, correlations between structural and functional connectivity were investigated distinguishing between synchronous and sequential activity of the nodes. The primary analysis encompasses applying different dynamical models to network architectures to explore how SC/FC correlations are shaped by variations in network topology, coupling strength, and intrinsic system parameters across excitable, chaotic, and oscillatory dynamics. A more detailed investigation was conducted on regular graphs of coupled logistic maps. Symbolic encoding of the initial dynamics was used to construct equivalent cellular automaton models, followed by an analysis of the structure of their resulting attractors. The influence of noise on SC/FC correlations was also explored. Finally, SC and the two types of FC were conceptualized in a hydrological case study. Structural and functional networks were constructed from data collected in the Walnut Gulch Experimental Watershed (Arizona, USA). SC/FC correlations served as metrics to describe event-level hydrological responses of the watershed after various rainfall events, and their relationships to hydrological quantities were analyzed.