In this paper, we examine the mathematical structure of chemical reaction networks with the goals of identifying reaction invariant states and determining their physical significance. A combined species-reaction graph/convex analysis approach is developed to find semi-positive invariant states associated with a reaction network. Application of this graphical/algebraic reaction network analysis approach to four different chemical processes reveals that reaction invariants can represent conserved quantities other than elemental balances. (C) 2018 Elsevier Ltd. All rights reserved.