  We examine a variant of hypergraphs that we call interfaced linear
hypergraphs, with the aim of creating a sound and complete graphical language
for symmetric traced monoidal categories (STMCs) suitable for graph rewriting.
In particular, we are interested in rewriting for categorical settings with a
Cartesian structure, such as digital circuits. These are incompatible with
previous languages where the trace is constructed using a compact closed or
Frobenius structure, as combining these with Cartesian product can lead to
degenerate diagrams. Instead we must consider an approach where the trace is
constructed as an atomic operation. Interfaced linear hypergraphs are defined
as regular hypergraphs in which each vertex is the source and target of exactly
one edge each, equipped with an additional interface edge. The morphisms of a
freely generated STMC are interpreted as interfaced linear hypergraphs, up to
isomorphism (soundness). Moreover, any linear hypergraph is the representation
of a unique STMC morphism, up to the equational theory of the category
(completeness). This establishes interfaced linear hypergraphs as a suitable
combinatorial language for STMCs. We then show how we can apply the theory of
adhesive categories to our graphical language, meaning that a broad range of
equational properties of STMCs can be specified as a graph rewriting system.
The graphical language of digital circuits is presented as a case study.
