Are all calculations graphs?
I wouldn't say that code is a graph.  I would say that graphs are a convenient way to represent some aspects of graphs.

There is a sense in which every computation on your computer can be expressed as a state machine: if your computer has 8 billion bits of memory, then there are at most $2^{8,000,000}$ possible states, so it can be considered as a state machine on that state space.  However, that probably isn't a very useful point of view.  Instead, we usually model computers as Turing machines (or in another way), and those cannot be expressed as a finite state machine.

The question of whether all computations are graphs doesn't seem well-defined to me.  Presumably graphs can be used to represent some aspects of computations, but that doesn't mean the calculation is a graph (or that it is nothing more than a graph).