  The transition towards a circular economy has gained importance over the last
years since the traditional linear take-make-dispose paradigm is not
sustainable in the long term. Recently, thermodynamical material networks
(TMNs) [1] have been proposed as an approach to re-design material flows based
on the idea that any supply chain can be seen as a set of thermodynamic
compartments that can be added, removed, modified or connected differently. In
this paper, we develop several circularity indicators of TMNs using a
graph-based formalism and illustrate their calculation through examples. The
paper source code is publicly available.
