Granulation for Graphs

In multi-resolution data handling, a less detailed structure is often derived from a more detailed one by amalgamating elements which are indistinguishable at the lower level of detail. This gathering together of indistinguishable elements is called a granulation of the more detailed structure. When handling spatial data at several levels of detail the gran-ulation of graphs is an important topic. The importance of graphs arises from their widespread use in modelling networks, and also from the use of dual graphs of spatial partitions. This paper demonstrates that there are several quite diierent kinds of granulation for graphs. Four kinds are described in detail, and situations where some of these may arise in spatial information systems are indicated. One particular kind of granu-lation leads to a new formulation of the boundary-sensitive approach to qualitative location developed by Bittner and Stell. Vague graphs and their connection with granulation are also discussed, and two kinds of vague graphs are identiied.