Computing direction of an edge after split-edge

Question

Let's say we have an edge with 2 vertices, v1 and v2. If I am in v1 I want the vector (v1, v2). If I am in v2, I want (v2, v1) (the opposite).

I have found some strange results in Blender, which means it is a bug or I am missing something. It is usually the second case, but here it is the case:

In the picture there are 3 vertices: A (-1,1,0), B(1,1,0) and C (1,-1,0). They are orthogonally connected: A - B - C.

I take the geometry and do split edges, so vertex B is duplicated, having: A - B , B' - C. Now I make use of Edge Vertices node to find out the other vertex in the pair. Two things happens:

1. Store Named Attribute node does not save the vertex 2 index. It is always 0
2. I marked with a red square in the picture. The vertex B (index 2), see himself as the other vertex in the edge, but the subtraction (= direction vector) seems to be correct.

I strongly suspect Blender is using the original Mesh when running Edge Vertices rather than the "split edge mesh".

So, is there any way to solve point 1 and 2?

Is there a better way to compute the direction I am looking forward? In a more complex case it is not correctly computed, but I could not find the minimal case to reproduce it.

Thanks in advance!

==============

As Robin Betts suggested:

It does not make any sense to me. It is the same problem I got with my solution.

========

Just for those with curiosity, here is the blender file

Answer 1

Personally, I think I'd want to be sure that whatever problem I was solving this way couldn't be solved more generally, purely in the Edge domain? The edge-end indices don't exist in the Vertex domain, so will evaluate as 0.

But in the special case of separated edges in an edge-only mesh, it seems the explicit (1-value) interpolation from Edge domain to Vertex domain works:

So, for example, you can make instances on extruded edges like this:

Answer 2

Robin Betts' solution has been true salvation for me. I tested it made some discovers and small modifications.

First of all, as you can see, the Node Tree (unchanged) outputs different results depending on the geometry. My goal was to create a geodesic dome with procedural structural parts. Though, to achieve the desired result, with Robin's Note Tree I had to remove faces from the mesh in Edit Mode.

On the left, in fact, you can see the result with the original geometry.

It is not clear to me why this is happening. I have, at least, two doubts:

1. On the left mesh (the working one) Split Edges node seems to work properly but there is no face anymore, so, what connected geometry elements is it splitting? Vertices? It is not what Blender documentation claims.

Like the Edge Split Modifier, the Split Edges node splits and duplicates edges within a mesh, breaking ‘links’ between faces around those split edges.

2. What went wrong with the left mesh? The Rotation passed in to the Instance on Points node, after all, is a quantity derived from the operation which members are the positions of the vertices of each edge. But observing the unexpected result it looks like the Edge Vertices node is (somehow) "out of scope" in this particular context.

Finally, I added two improvements to Robin's Node Tree (one of which I am not sure is required).

1. I added a basic scale operation such that the arrows fill the entire edge length.
2. I added a Vector Math node with Normalize operation applied to the rotation vector.

This is the link with the file (I am using GDrive because blend-exchange.com seems to take eons to upload).

https://drive.google.com/file/d/11W8NQLgH1OAJ1_-hfDsh4je_Sk4bar8N/view?usp=sharing