Robots are rapidly evolving from factory workhorses to robot-companions. The future of robots, as our companions, is highly dependent on their abilities to understand, interpret and represent the environment in an efficient and consistent fashion, in a way that is comprehensible to humans. This paper is oriented in this direction. It suggests a hierarchical probabilistic representation of space that is based on objects. A global topological representation of places with object graphs serving as local maps is suggested. Experiments on place classification and place recognition are also reported in order to demonstrate the applicability of such a representation in the context of understanding space and thereby performing spatial cognition. Thus the theme of the work is representation for spatial cognition.