  We use the framework of "props" to study electrical circuits, signal-flow
diagrams, and bond graphs. A prop is a strict symmetric monoidal category where
the objects are natural numbers, with the tensor product of objects given by
addition. In this approach, electrical circuits make up the morphisms in a
prop, as do signal-flow diagrams, and bond graphs. A network, such as an
electrical circuit, with $m$ inputs and $n$ outputs is a morphism from $m$ to
$n$, while putting networks together in series is composition, and setting them
side by side is tensoring. Here we work out the details of this approach for
various kinds of electrical circuits, then signal-flow diagrams, and then bond
graphs. Each kind of network corresponds to a mathematically natural prop. We
also describe the "behavior" of electrical circuits, bond graphs, and
signal-flow diagrams using morphisms between props. To assign a behavior to a
network we "black box" the network, which forgets its inner workings and
records only the relation it imposes between inputs and outputs. The process of
black-boxing a network then corresponds to a morphism between props.
Interestingly, there are two different behaviors for any bond graph, related by
a natural transformation. To achieve all of this we first prove some
foundational results about props. These results let us describe any prop in
terms of generators and equations, and also define morphisms of props by naming
where the generators go and checking that relevant equations hold. Technically,
the key tools are the Rosebrugh--Sabadini--Walters result relating circuits to
special commutative Frobenius monoids, the monadic adjunction between props and
signatures, and a result saying which symmetric monoidal categories are
equivalent to props.
