8 C H A P T E R   1 Figure 1.1 The statement,  Napoleon is emperor,  in RDF. equivalent  from  a  mathematical  standpoint.  And  because  programming  is  a way of creating mathematical models of actions, this also means that to a pro- gram, they are equivalent. To a mathematician, graphs are very rarely unique. They can be transformed into other graphs, and operations can be conducted on them. Algebraic opera- tions are used to model computer software. This means that there is a well- established way of going from the graph format of RDF to a way of handling it in the computer. The more you want to say, however, the more complex it becomes. A graph does not have to be two-dimensional, either; it can have n dimensions and be arbitrarily complex. Of course, this slows down processing and decreases the readability. But it is possible to express quite complex relationships as graphs. Here is a graph of the statement that Napoleon first was a lieutenant, then a general, then a consul, and finally emperor: Napoleon S lieutenant S general S consul S emperor Of course, the graph could be drawn differently. This graph actually does not refer back to Napoleon, but refers from one concept to the other. There  is  an  entire  mathematical  theory  associated  with  graphs,  how  they should be handled, what transformations are allowed and possible, and so on. The operations you can do on RDF descriptions are described in graph theory. 69528_CH01Ix  4/6/2001 8:15 AM  Page 8