Utility–service provision is a process in which products are transformed by appropriate devices into services satisfying human needs and wants. Utility products required for these transformations are usually delivered to households via separate infrastructures, i.e., real-world networks such as, e.g., electricity grids and water distribution systems. However, provision of utility products in appropriate quantities does not itself guarantee that the required services will be delivered because the needs satisfaction task requires not only utility products but also fully functional devices. Utility infrastructures form complex networks and have been analysed as such using complex network theory. However, little research has been conducted to date on integration of utilities and associated services within one complex network. This paper attempts to fill this gap in knowledge by modelling utility–service provision within a household with a hypergraph in which products and services are represented with nodes whilst devices are hyperedges spanning between them. Since devices usually connect more than two nodes, a standard graph would not suffice to describe utility–service provision problem and therefore a hypergraph was chosen as a more appropriate representation of the system. This paper first aims to investigate the properties of hypergraphs, such as cardinality of nodes, betweenness, degree distribution, etc. Additionally, it shows how these properties can be used while solving and optimizing utility–service provision problem, i.e., constructing a so-called transformation graph. The transformation graph is a standard graph in which nodes represent the devices, storages for products, and services, while edges represent the product or service carriers. Construction of different transformation graphs to a defined utility–service provision problem is presented in the paper to show how the methodology is applied to generate possible solutions to provision of services to households under given local conditions, requirements and constraints.