This paper studies the dynamics of a multi-module floating airport with flexible connectors using the network theory. A mathematical model for a chain-type topology structure is developed by using the wave theory, and the models of a single floating module and the connector and mooring system. The nonlinear dynamics of the floating airport and the connector force are studied. A remarkable phenomenon of amplitude death is observed, as a weak oscillation state of all floating modules, an important state for the system global dynamic stability. The parametric domain for the onset of amplitude death is identified, and the effects of the wave height and the number of the floating modules on the dynamic stability are discussed. An application of the network theory in the marine engineering is illustrated with the introduction of a new concept for global dynamic stability for the floating airport.