%0 Generic %A Bonchi, F %A Piedeleu, R %A Sobocinski, P %A Zanasi, F %C Vancouver, BC, Canada %D 2019 %F discovery:10081075 %I IEEE %T Graphical affine algebra %U https://discovery.ucl.ac.uk/id/eprint/10081075/ %X Graphical linear algebra is a diagrammatic language allowing to reason compositionally about different types of linear computing devices. In this paper, we extend this formalism with a connector for affine behaviour. The extension, which we call graphical affine algebra, is simple but remarkably powerful: it can model systems with richer patterns of behaviour such as mutual exclusion—with modules over the natural numbers as semantic domain—or non-passive electrical components—when considering modules over a certain field. Our main technical contribution is a complete axiomatisation for graphical affine algebra over these two interpretations. We also show, as case studies, how graphical affine algebra captures electrical circuits and the calculus of stateless connectors—a coordination language for distributed systems %Z This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.