Please do NOT use all capital letters in post title, - other posts are not less important than yours. Make it a habit to read docs and show some of your own effort and code to solve the problem, even if it does not work. Also please try to limit one post to one question.
Simplest way is to define theorems in the notebook:
th1 = "Theorem 1
---------------
Some text
Some text";
th2 = "Theorem 2
---------------
Some text
Some text";
Then if you click on the edge:
Graph[{
PopupWindow[1 -> 2, th1],
PopupWindow[2 -> 3, th2],
3 -> 1},
GraphStyle -> "SmallNetwork",
DirectedEdges -> True]
a popup window will appear:
To open an external file use Button instead of PopupWindow and put SystemOpen inside it.
