Chemical reaction systems of mass action type are polynomial differential equations. The structure og the polynomials is determined by graphs. Because of the graph theoretic structure and the polynomial structure special results are known. I will explain how the latttice suggests Lyapunov functions and how the lattice may be investigated with Hermite normal form. Secondly, I will explain the importance of deformed toric varieties in the work by Clarke on stability of reaction networks and Hopf bifurcation. Computational examples like the Calcium oscillation will be given.