in this work i discuss the $sigma-$function of a graph. i will discuss the $sigma-$function and the $\vartheta-$function of lov\'asz, cliques, coloring, and much more. i will show the results of experiments (pictures!), give some basic structure theory, and mention conjectures and open problems. if time permits i will talk about applications to graph drawing and clique finding. this talk should be accessible to all. this is joint work with fan chung.