Transportation is an example of a typical, open, fluid complex network system. Expressways are one form of complex transportation networks, and expressway service areas serve as infrastructure nodes in the expressway transportation network; hence, their construction has a significant impact on tourism development and utilization. Domestic and foreign studies on complex transportation networks have mostly been conducted from the perspective of railways, air transport, and urban transportation but seldom on expressway transportation networks. This study employed complex network theory, social network analysis, kernel density analysis, and bivariate autocorrelation to characterize the spatial structure of expressway transport networks in terms of geographical centrality. By innovating the coupling of geographical centrality and passenger flow centrality in clustering, the study also quantitatively analyzed the differences between the geographical advantage and actual passenger flow advantage of China’s Guizhou expressway transportation network to analyze the tourism utilization potential of expressway service areas. We found that (1) the geographical centrality of the Guizhou expressway transportation network ranged from −1.28 to 3.33, and its distribution shows a single-core, polyconcentric dispersed spatial structure; (2) the passenger-car flow rate ranged from 15,000 to 3.66 million, and its distribution showed a dual-core, polycentric dispersed structure that is weakly concentric; and (3) there was a positive correlation of 0.22 between the geographical centrality and passenger flow of the Guizhou expressway transportation network, which showed seven cluster types—“high-high,” “moderately high-high,” “low-high,” “moderately low-high,” “high-low,” “moderately high-low,” and “low-low”—for which seven corresponding models of tourism development were proposed. This study broadens the practical application of traffic network complexity research and provides a scientific basis for upgrading and transforming the Guizhou expressway transportation network as well as for developing composite tourism uses for expressway service areas.