  This paper introduces a model that identifies spatial relationships for a
structural analysis based on the concept of simplicial complex. The spatial
relationships are identified through overlapping two map layers, namely a
primary layer and a contextual layer. The identified spatial relationships are
represented as a simplical complex, in which simplices and vertices
respectively represent two layers of objects. The model relies on the simplical
complex for structural representation and analysis. To quantify structural
properties of individual primary objects (or equivalently simplices), and the
simplicial complex as a whole, we define a set of centrality measures by
considering multidimensional chains of connectivity, i.e. the number of
contextual objects shared by a pair of primary objects. With the model, the
interaction and relationships with a geographic system are modeled from both
local and global perspectives. The structural properties and modeling
capabilities are illustrated with a simple example and a case study applied to
the structural analysis of an urban system.
