River connectivity is essential for maintaining fertile floodplains, healthy ecosystems, and human activities, particularly in semi-arid regions, where water flow is often intermittent. Despite its importance, very few studies have attempted to quantify connectivity at the scale of individual rainfall-runoff events. In this study, we present a novel framework for exploring synchronous and sequential connectivity, to capture the hydrological response of a system. We distinguish between structural (SC) and functional (FC) connectivity, by constructing structural networks utilizing topographic data from the Walnut Gulch Experimental Watershed in Arizona, USA, and correlation-based functional networks using high-resolution runoff data. We examine how SC/FC relations vary across rainfall events and how they relate to the hydrological responses of the system. We apply unsupervised learning algorithms to classify rainfall events and identify the corresponding dominant runoff connectivity patterns within each cluster. The results of our analysis showed that large rainfall events typically exhibit higher sequential SC/FC correlation values, indicating widespread system connectivity. In contrast, short, intense storms tend to produce localized runoff connectivity, which are characterized by dominant synchronous SC/FC relations. High SC/FCseq correlation values (> 0.5) combined with moderate SC/FCsync (≈0.3) typically indicate that water flow reached the watershed outlet, however, maximum SC/FCseq is not necessarily associated with peak discharge at the watershed outlet. The clustering analysis revealed further statistically significant patterns linking rainfall characteristics with distinct SC/FC correlation regimes. Due to its flexibility, our approach suggests a general framework for analyzing connectivity dynamics in any river network with an intermittent flow regime.