1 Introduction: the problem Space syntax provides a method for partitioning a spatial system into relatively independent but connected subspaces so that the importance of these subspaces can be measured in terms of their relative nearness or accessibility (Hillier and Hanson, 1984). It is similar to a wide class of models for measuring spatial interaction, developed over the last fifty years as part of social physics, which derive relative accessibility from the underlying graphtheoretic structure of relations, usually based on the Euclidean distances between small areas (Wilson, 1998). It differs from this class, however, in three significant ways. First, the subspaces or small areas which compose the basic representational elements in space syntax are ill defined. The spatial elements used are not directly observable and measurable and, although they depend upon the geometric properties of the space, there is no agreed or unique method for their definition. Second, spaces are not collapsed to nodes or points but are first defined by lines which are then considered as nodes. Third, the relations between these components or nodes are defined in terms of their topology and, although Euclidean distance is implicit, relations are measured in binary termsöwhether they exist or not.In this paper we will focus entirely on the first problem which involves defining the spatial components used in subsequent relational analysis. We will introduce methods which resolve the problem of deriving a unique set of elements, thus enabling their automatic definition. These methods extend quite naturally to the second and third problems in that representing lines as nodes is no longer necessary. The method we introduce suggests that the relative importance of lines associated with subspaces is