Not sure if this is the most answerable question, but it is worth a shot. I am slowly getting into math, and have been interested in graph theory for a while. I use it in programming all the time.
From a programming perspective, it seems that a graph is a higher level abstraction on top of a tree, and a tree is a higher level abstraction on top of a list. By higher level, I mean it can be applied to more real-world problems. So in a sense, a tree builds on a list, and a graph builds on a tree.
The graph is by far the most widely applicable to real-world problems. But I am wondering, are there any recent developments in math that build on top of the graph?
list -> tree -> graph -> ???
Are there any objects in math that are abstractions on top of graph in this same sort of way? If so, I would really like to read about them to learn about the new directions in which people are taking graphs.
The reason is, while graphs are much more applicable to real-world problems than trees or lists, they still fail to concisely describe highly variable domains. Examples are things like concisely modeling the hierarchical/temporal evolution of multi-scale models (biology, physics, chemistry, all three together, etc.). Wondering if there are any mathematical developments building on top of graph-theory to make it easier to elegantly describe things like this.
A function is definitely more applicable than a graph, and more general. However, it doesn't have the same sort of hierarchical/relational/nested structure that a graph does (though you can obviously nest and relate functions). Wondering if there is a higher level of abstraction on top of a graph, or something along those lines.