Feature models are used to represent the variability and commonality of software product lines (SPL), and to decide on the configuration of specific applications. Several variants based on tree or graph hierarchical structures have been proposed. These structures are completed with additional constraints, generally expressed in parallel with the feature diagram. This paper proposes the use of hypergraphs to integrate both concepts in a unique characterization. Therefore, the definition, validation and selection of feature configurations can be internally based on the hypergraph properties and well-known algorithms, while the concrete visual syntax remains unchanged for domain engineers. The implemented hypergraph algorithms have been tested using a complete set of feature diagrams. Finally a feature meta-model can be derived directly from the formal definitions, providing the foundations for building feature modeling tools.