Comment How About System Tools Like Causal Loop Modeling? (Score 1) 63
If it were me, I would redefine the goal slightly. It is not just the dependencies. It is the behaviour of the overall system, the collection of application components, that you need to be able to explain. In fact, if you want to know which components you can remove or tweak, you actually need to understand the business processes they are supposed to be supporting.
Theoretically, the raw business processes of each company will represent less complexity than the system of application components you need to describe. These business processes would provide "overlays" that could help you to see the extraneous components of your "application system".
Causal Loop Modeling (CLM) might be the right tool, specifically because you want to establish how a change in one part of the "application system" affects everything else. CLM is a successor to Stock and Flow modeling, but you can use it by istelf to explain system behaviour. It works especially well when there are feedback loops present that create complex behaviours such as goal seeking, cyclical or seasonal variation, and sudden growth or decline.
However, you could simplify the CLM approach if you leave out the notations that define positive and negative forces. Essentially, you create a chart that connects every component to its upstream and downstream components. What you are left with is a diagram showing each component with many inflows and outflows.
The way this is useful is to first note the components that have the most inflows. These are the "driven" components, the ones most affected by change.
The components with the most outflows have the most influence on the others. Changes to these components create significant impact to the overall system.
Armed with this information you can really start to establish where you can trim and where you can not. You can also start to identify where small changes can have a big influence. Like a vaccination: small change-big effect. In effect, you find the points of leverage in the system. That is where is starts to get really interesting.
Hope this helps to get you started, or at least to provide a different perspective. If this interestes you, post questions and I will try to answer them.