Non-manifold topological representations can provide a single unified representation for mixed dimensional models or cellular models and thus have a great potential to be applied in many application areas. Various boundary representations for non-manifold topology have been proposed in recent years. These representations are mainly interested in describing the sufficient adjacency relationships and too redundant as a result. A model stored in these representations occupies too much storage space and is hard to be manipulated. In this paper, we proposed a compact hierarchical non-manifold boundary representation that is extended from the half-edge data structure for solid models by introducing the partial topological entities to represent some non-manifold conditions around a vertex, edge or face. This representation allows to reduce the redundancy of the existing schemes while full topological adjacencies are still derived without the loss of efficiency. To verify the statement above, the storage size requirement of the representation is compared with other existing representations and present some main procedures for querying and traversing the representation. We have also implemented a set of the generalized Euler operators that satisfy the Euler-Poincare formula for non-manifold geometric models.