The dynamics and mechanics of networks depend sensitively on their spatial connectivity. To explore the effect of connectivity on local network dynamics, we prepare transient polymer networks in which we systematically cut connecting bonds. We do this by creating networks formed from hydrophobically modified difunctionalized polyethylene glycol chains. These form physical gels, consisting of flowerlike micelles that are transiently cross-linked by connecting bridges. By introducing monofunctionalized chains, we can systematically reduce the number of bonds between micelles and thus lower the network connectivity, which strongly reduces the network elasticity and relaxation time. Dynamic light scattering reveals a complex relaxation dynamics that are not apparent in bulk rheology. We observe three distinct relaxation modes. First we find a fast diffusive mode that does not depend on the number of bridges and is attributed to the diffusion of micelles within a cage formed by neighboring micelles. A second, intermediate mode depends strongly on network connectivity but surprisingly is independent of the scattering vector q. We attribute this viscoelastic mode to fluctuations in local connectivity of the network. The third, slowest mode is also diffusive and is attributed to the diffusion of micelle clusters through the viscoelastic matrix. These results shed light on the microscopic dynamics in weakly interconnected transient networks.