about theorem graphs

**notes about graphs**

  * The connections in the graph represent links that generally fall into the 
    following categories:
    * pedagogic links (similar to object graphs, often but not necessarily 
      coincide with structural links, best suited for syllabus organization)
    * structural links (object graphs, formal repartition of connections among 
      objects properties and operations).
    * logical links ( -> theorem paths , do not coincide with object graphs)
    * historical links (do not necessarily coincide with theorem path graphs)
      * a variant of this is a full historical graph , where new types of nodes
        are used to represent persons who contribute to theoretic development, 
        writings and other research artefacts, and a timeline. 


  * Of the different kinds of graphs, some stand out more : 
    * __**1. Theorem path graphs:**__ 
      * show how axioms lead to theorems and how the latter lead to more theorems. 
      * they also show how different concepts or formalisms lead to different 
        theories and where a given theory is situated with respect to other 
        theories, in terms of "lead to" relationships and influence, or borrowed 
        concepts and formalisms.
      * These graphs also often coincide with the (actual) historical developmental 
        sequence of the theories shown. 
      * This can be emphasized using a time line with actual dates or year dates 
        to highlight the historical sequence of developments. 
      * Nonetheless theorem paths are not always ordered in historical sequence, and 
        should be distinct from historical graphs for this and for other reasons
        * eg, historical graphs also use person nodes, which are not always needed 
          or desirable in theorem path graphs.
      * Theorem graphs are particularly useful at the high level, where inspection 
        shows interdisciplinary connections and general paradigmatic and formalism 
        developments in mathematical or physical theories.
    * __**2. Object graphs:**__
      * These should reflect the basic notion that mathematical objects or classes 
        of objects (and by extension mathematical theories) are synthesized from sets 
        and a set of properties and for which certain operations are defined which
        are often maps. 
      * in the case of object graphs, The drawing itself,is a structuring process 
        that reflects the structure of the mathematical or algebraic theory.
        * akin , though in a less formal way, to object-oriented class diagrams. 
          The main difference is that common operations and properties are listed 
          separately from classes. Also, object graphs do not have to include
          object maintenance and communication patterns found in OO class diagrams.

  * aesthetic note: our philosophy regarding the choice of graph colors (color 
    styling) is sabr aghwar el-blandness.

  * graph examples - all are snippets : 
    * theorem_graphs
    * object_graphs
    * historical graph.