What's the definition of system? I am wondering if a representation like a graph be considered a system, or a system needs to have some kind of effect on something and not merely represent something. Looking at the definition, it seems that a system can be a graph with two elements in it.
In accordance to the Systems Theory, this might be the most common definition: a system is a set of interrelated parts.
In simple words, a system is a group of things related by something. From a simpler perspective, given that any possible thing in nature (or even any idea) can be split in parts, any object can be considered a system. Some say that the definition is fractal: subsystems are also systems that have parts ad infinitum, and supra systems are equivalent. There are no sub-sub-sub...-systems; just systems. At any level, all things are part of something bigger, and have smaller parts.
Relationships are a form of order, that's why the term system is also used to feature organised wholes: a philosophical system; an informative system, my personal accounting system; Kant had a mania for systematizing knowledge.
So, "butter", "flour", "salt" do not conform a system as such. But if that is my groceries list, it can be considered a system since they are related by some organising rule. Or they can be the essential components of a cake; so, the cake being the system in the case.
As you see, the term system can be loosely used in multiple senses, but it is mostly used to characterize organisation.
So, a graph can be considered a system from multiple perspectives. Semantically, it can be a system, since it is a set of interrelated nodes. From a syntactic perspective, it can also be a system, cause it is a set of graphical elements that represent a behavior. Even from the perspective of the physical thing, a graph might be a piece of paper with ink lines over it, expressing a sense. These expressions are acceptable: the graph system; the system graph; the graph systematizes the behavior; the graph is a system of states; it can be systematized in a graph/representation, etc.
But a pure graph, as such, as an atomic element (that is, that doesn't have parts), without any possible relation, in a context where nothing else exists, can hardly be considered a system.
There are additional features that systems might exhibit, but that are not commonly included in the definition:
a) inputs and outputs (a coffee machine is a set of mechanical parts accepting coins and outputting coffee). Even abstract systems have inputs and outputs, but they can present some difficulties to be identified, the notions of object-subject interaction are essential for that. Loosely, the input in a graph is the attention that focuses in some node of the graph, and moves according to its rules, and the output might be the fact of finding the current state that corresponds to the input.
Some say that when systems lack of of inputs and outputs, can be considered "closed systems". But that is something which doesn't exist in nature. Just think that any atom interacts with any other (perhaps by an infinitesimal amount, but it interacts anyway), or that your body is exerting attraction even on the most remote galaxy in the universe. Closed systems are mostly theoretical constructs that prove useful in some contexts (e.g. thermodynamics, electronics).
b) a teleological foundation (a goal). Around 1970, many theorists used a different concept: a system is a set of parts with a shared goal. But goals are considered subjective in philosophy. So, if the earth would be a system, then it was intended to exist with a goal, then an intention would be implicit, and even more, a creator. As you see, such element intr a lot of undesirable considerations into the concept. So, currently, the goal is not anymore used as part of the definition.