New service enterprises are digitally connected value cocreation networks. From this perspective, we analyze how hyper-network models can lead to new understanding for service science. A hyper-network is an integration of multi-layered (role-based) connections of members in a community, such as the Internet and an ecosystem. Hyper-network analysis creates multi-dimensional understanding of network properties, such as the centers of connections between layers (the hyper-hubs or ―value wormholes‖) and the shortened distance between nodes (or, the centrality of members) due to such value wormholes. This paper shows that the common practices of adding new links to an existing random graph (e.g., merging FaceBook with other social networking/ecommerce sites) is equivalent to creating a new layer of a hyper-network; and hyper-network analysis promises to reveal otherwise hidden social structures and thereby yield more accurate estimates for average distance and other properties. Estimation formulae are provided for determining the average vertex-vertex distance and average vertex degree. On this basis, the paper proves that hyper-networks enhance ordinary random graphs in these measures, and hence can probably model real-world social networks better than the previous two-dimensional graphs. The paper suggests that all human networks, including social and economical, maybe fundamentally hyper-networks.