The study of network representations of physical, biological, and social phenomena has developed rapidly in recent years. This paper presents a review of important results and methods of the science of networks with an application to the field of socio-economic systems. The basic definitions and computational techniques are described and the effects of a network’s topology on its dynamic properties are examined and illustrated using a tourism destination as a case study (Elba, Italy). A static structural characterization of the network formed by destination stakeholders is followed by a dynamic analysis of the information diffusion process. The outcomes and the implications of this analysis for improving destination management are discussed.