Currently, graph_mermaid can throw an error when subgraphs are deeply nested, due to its way of tracking subgraph names and its order of processing edges. We encountered this in production with a large graph which had a couple of levels of subgraphs and many edges.

See the nodes/edges fixture added in graph_mermaid.test.ts, which is a minimal reproduction of one part of our graph, and will throw the following error on main branch:

Found duplicate subgraph 'fooGenericSearch' -- this likely means that you're reusing a subgraph node with the same name. Please adjust your graph to have subgraph nodes with unique names

The graph (and original langgraph code that generated it) is valid, and doesn't have a duplicate subgraph, but the subgraph/prefix handling misrecognizes it as duplicate when traversing and tracking the set of subgraphs.

This PR fixes that, and can now render the graph correctly; and also pre-orders the edges so that subgraphs will appear in their correct nesting, which wasn't necessarily the case before.

Without the additional edge reordering, the test graph here was not properly nested:

due to incorrect ordering of subgraphs (excerpt):

      subgraph fooTool
      subgraph fooGenericSearch
         ...
      end
      subgraph fooSearchSource
         ...
      end
        ...
      end

With the fix, it is, thanks to ordering edges by depth before traversal:

          subgraph fooTool
          subgraph fooSearchSource
          subgraph fooGenericSearch
              ...
          end
              ...
          end
              ...
          end

I was able to test this rendering on our very large application graph and there were no unintended side effects / regressions; would be happy to have even more test cases for example graphs if needed--this particular script had little in the way of existing tests.