I'm dealing with a particular optimization problem at work (financial scorecards), and I noticed that my dataset can be set up as a set of DAGs, where the scorecards for each customer comprise a customer-specific tree. However, I'm unsure as to whether that's a useful characterization.
To that extent, in a more broad sense, I was wondering: what types of question does graph theory best answer? I can think of a few applications, namely:
- find minimum distance between nodes (e.g., directions from point A to point B)
- optimal path for traverse entire graph and hitting all nodes while minimizing distance (e.g., traveling salesman)
- given an incomplete graph, determine whether some nodes should be connected (e.g., "find my friends" on facebook/linkedin)
Are there any other major applications?