Multiscale Geographic Information with Multigraph of Multigraphs

Multiscale resolution database MRDB include not only several levels of details (ie preciseness), but also several layers of peculiarity. The data preciseness means the variable levels of details for the fixed set of attributes. Less details leads to data aggregation, more details leads to data de-aggregation. The data peculiarity means the growing and reduction of the number of variable attributes for the fixed level of details. More attributes leads to higher hierarchizated data (better, finer structural data trees), less attributes leads to less organized data. We propose to consider the concept of a multiscale to be derivable from the more primitive above concepts of preciseness and peculiarity. A mathematical model of multiscale database is proposed, in terms of multigraph theory, with idealized mathematical distinction among the concept of preciseness, and the concept of peculiarity. We relate conceptually the grade of the preciseness with the internal structure of the graph of graphs. Instead, the grade of the peculiarity we wish to relate with the external structure of the multigraph (or multi-hyper-graph). Hierarchical data information we propose to encode into external structure of the multigraph, and this goes beyond the usual hierarchical tree. The hierarchical information is illustrated by means of a linking the thematic maps of the same family of objects.