  String diagrams are an increasingly popular algebraic language for the
analysis of graphical models of computations across different research fields.
Whereas string diagrams have been thoroughly studied as semantic structures,
much less attention has been given to their algorithmic properties, and
efficient implementations of diagrammatic reasoning are almost an unexplored
subject.
  This work intends to be a contribution in such a direction. We introduce a
data structure representing string diagrams in terms of adjacency matrices.
This encoding has the key advantage of providing simple and efficient
algorithms for composition and tensor product of diagrams. We demonstrate its
effectiveness by showing that the complexity of the two operations is linear in
the size of string diagrams. Also, as our approach is based on basic linear
algebraic operations, we can take advantage of heavily optimised
implementations, which we use to measure performances of string diagrammatic
operations via several benchmarks.
