A port graph
A special type of prop where morphisms are open, directed, acyclic port graphs \((V, in, out, i)\)
\(V\) is a set of vertices
functions \(V \xrightarrow{in, out} \mathbb{N}\) give the in degree and out degree of each vertex
A bijection \(\bar m \sqcup O \xrightarrow{i} I \sqcup \bar n\), where \(I = \{(v,i)\ |\ v \in V, 1 \leq i \leq in(v)\}\) and \(O=\{(v,i)\ |\ v \in V, 1 \leq i \leq out(v))\}\) are the vertex inputs and vertex outputs, respectively.
Furthermore, an acyclicity condition:
Use the bijection \(i\) to construct the internal flow graph: a graph with an arrow \(u \xrightarrow{e^{u,i}_{v,j}} v\) for every \(i,j \in \mathbb{N}\) such that \(i(u,i)=(v,j)\)
This graph must be acyclic