This work introduces a graph-based approach to the representation of evolving entities in space and time. At an abstract level, the model makes a distinction between filiation and spatial relationships between entities, while at the database level, it stores derivation relationships and determines continuation and spatial relationships in time. An extended relational database specification implements the spatio-temporal graph model. A formal language models integrity constraints that are inherent to the model and those that are semantic and application dependent. The satisfiability of these constraints is studied and an algorithm for checking consistency of spatio-temporal graph is provided. An experimental evaluation shows the potential of the model.