Let's get more specific now.

Let \$$t\$$ be a transition, and Stoich(\$$t\$$) be its stoichiometric vector.

For a species \$$z\$$, let InpDegree(\$$t,z\$$) be the number of places that \$$t\$$ inputs from \$$z\$$, and OutDegree(\$$t,z\$$) be the number of places \$$t\$$ outputs to \$$z\$$.

Let \$$x \in \mathbb{N}^S\$$ be a definite state, and let \$$x' = x\$$ + Stoich(\$$t\$$).

If \$$x'\$$ contains any negative components, then it is outside of \$$\mathbb{N}^S\$$, and it is not a valid state. That indicates that the transition \$$t\$$ doesn't have a sufficient number of input tokens in \$$x\$$ to fire.

If however \$$x'\$$ does belong to \$$\mathbb{N}^S\$$, then we add an edge \$$e(t,x,x')\$$ from \$$x\$$ to \$$x'\$$ in the graph.