We introduce the Mangrove Topological Data Structure (Mangrove TDS) framework for modeling simplicial complexes. It is based on a graph-based representation of the data structures, called mangroves, which ensures an extensible representation of a data structure for simplicial complexes. Mangroves can be easily customized for any modeling need, including the efficient representation of non-manifold shapes, and of those simplices, not directly encoded in a mangrove, that we call ghost simplices. We discuss here the properties of this framework, and current and future developments.