Jesper
S7-Graph is Siemens' name for their implementation of the IEC61131-3 SFC (Sequential Function Charts) language. (Except I notice PLCOpen and the IEC have stopped referring to it as a 'language', and say it should be regarded as a "method for structuring control programs".)
It's a very visual tool designed ideally for situations where you have a process with a specific procedural path - do this, wait for the response, now move on to that, check the feedback, now do the next thing ... and so on. It encourages you to lay out the idealised control flow for everything in the machine/plant. The step/transition method also makes fault-finding really easy. The process is stuck at a step? No problem: the next transition hasn't come true. That's it. No more wading through yards (sorry, metres) of code to find out.
Hi-Graph on the other hand is a Siemens' own-brand programming language with no counterpart in the IEC61131 standard. I think it was developed in conjunction with some universities in Germany plus some input from big German customers of Siemens like VW and BMW. It is also very visual, but instead of the strict SFC approach of one step / one transition, Hi-Graph is more of a state machine approach. Define your process or operation as a series of related states, and then define the conditions which would cause you to leave State 1 and go to State 2. And State 3. And State 4. etc. Now do the same for State 2, and so on. Its evry good at dealing with processes where there is no consistently predictable path through them, but you do need to prevent 'accidental' activation of states. If you don't explicitly code a transition between states it won't ever happen.
Both S7-Graph (and all other SFC compilers I've seen) and Hi-Graph carry a memory overhead, but if your process justifies them, the advantages are worth it and memory is cheaper than downtime.
Regards
Ken.