Can input-output matrices optimize bidirectional search?

Given a bidirectional search on a weigthed digraph, could a modified input-output matrix guess what nodes are more likely to belong to the shortest path and the search be done through these nodes first?

I thought of doing this in two ways:

1. Give "capital" to each node proportional to how many edges are connected to it, the flow of "capital" should follow the direction of the edge, the "capital" will be distributed inversely proportional to the weight of each edge, and the most "valued" vertices should be considered first for the search.
2. Give the same "capital" for each node, the flow of "capital" is the opposite of the directions of the edges, the "capital" is distributed directly proportionally to the weight of each edge, and least "valued" vertices should be considered first for the search.

Does it works?

• Please edit your question to add a self-contained definition of what is an "input-output matrix" in this context, how you would apply it to this problem, and how you would "guess" which nodes. Please explain this in a form that doesn't require prior familiarity with economics. I find your two bullet points very vague: e.g., for 1., it's not clear how you will translate that into an algorithm (I don't know how to translate "flow .. should follow" into computer code).
– D.W.
Oct 30, 2022 at 20:57