Complex simple Lie algebras are characterised by their Dynkin diagrams and same is true for affine Kac-Moody algebras also. Right angled artin groups, Coxeter groups and many other algebraic structures carries an associated graph and these graphs are concise way to present these groups. My question is what are the other mathematical structures in which there is always an associated graph and the graph reflects many properties of the structure. If anybody can quote explicit results regarding this that will be vey helpful.
Thanks a lot for your time.
I hope I explained my question better.