  Reaction networks (RNs) comprise a set $X$ of species and a set $\mathscr{R}$
of reactions $Y\to Y'$, each converting a multiset of educts $Y\subseteq X$
into a multiset $Y'\subseteq X$ of products. RNs are equivalent to directed
hypergraphs. However, not all RNs necessarily admit a chemical interpretation.
Instead, they might contradict fundamental principles of physics such as the
conservation of energy and mass or the reversibility of chemical reactions. The
consequences of these necessary conditions for the stoichiometric matrix
$\mathbf{S} \in \mathbb{R}^{X\times\mathscr{R}}$ have been discussed
extensively in the literature. Here, we provide sufficient conditions for
$\mathbf{S}$ that guarantee the interpretation of RNs in terms of balanced sum
formulas and structural formulas, respectively.
  Chemically plausible RNs allow neither a perpetuum mobile, i.e., a "futile
cycle" of reactions with non-vanishing energy production, nor the creation or
annihilation of mass. Such RNs are said to be thermodynamically sound and
conservative. For finite RNs, both conditions can be expressed equivalently as
properties of $\mathbf{S}$. The first condition is vacuous for reversible
networks, but it excludes irreversible futile cycles and - in a stricter sense
- futile cycles that even contain an irreversible reaction. The second
condition is equivalent to the existence of a strictly positive reaction
invariant. Furthermore, it is sufficient for the existence of a realization in
terms of sum formulas, obeying conservation of "atoms". In particular, these
realizations can be chosen such that any two species have distinct sum
formulas, unless $\mathbf{S}$ implies that they are "obligatory isomers". In
terms of structural formulas, every compound is a labeled multigraph, in
essence a Lewis formula, and reactions comprise only a rearrangement of bonds
such that the total bond order is preserved.
