Say I have a directional tree with the following edges:

nodeA --> nodeB

nodeA --> nodeC

nodeB --> nodeD

nodeC --> nodeE

nodeE --> nodeD

This means that the following nodes are of the following generations:

nodeA = 1

nodeB = 2

nodeC = 2

nodeD = 3, 4

nodeE = 3

What would be an appropriate term to call a visualization of this type of graphical structure, where one axis is constrained to generation count? For example, the root node (node A) is at x=1. Then node B and C are at x =2. Node E is at x=3. Node D is repeated in this visualization; one representation is at x=3, the other at x=4. All edges are included as usual between the appropriate nodes.

Are there any software available to produce this type of visualization?

Is there an standardized (or at least eloquent) way to specify such a visualization that can handle these "repeated" nodes while constraining one axis to generation count?

I'm not sure I understand the question, but this doesn't seem like a tree, 'A' is connected to 'D" by two paths.

Okay, I am editing the question. What I want to know is, what would be an appropriate term to call a visualization of this type of graphical structure, where one axis is constrained to generation count. For example, the root node (node A) is at x=1. Then node B and C are at x =2. Node E is at x=3. Node D is repeated in this visualization; one representation is at x=3, the other at x=4.

Is there an standardized (or at least eloquent) way to specify such a visualization that can handle these "repeated" nodes and constrain generation counts to one axis?

I guess we cross-posted. My answer below might give you some general clues. I don't know of a standard way to do the visualisation you are aiming for.

Thank you, David. I see what you mean about me misnaming it as phylogenetic. The visualization that I am thinking of, then, is a visualization of a simple cyclic graph, where the nodes are constrained by edge distance from the root node. Do you think that is the most standardized/eloquent/specific way to say it?

Also, thank you for your input that you don't know of a standard way to do this type of visualization. Are you saying that you do not know of any software that can accomplish such a visualization? (I only ask because I am working on making some now, and don't want to "reinvent the wheel") :o)

I have to confess, I don't quite grasp what you are trying to do. If nodes are going to be placed based on their path-length from the root then some nodes would appear multiple times, which is not the normal way of representing a graph. I don't know of any software that will do it with some kind of hack to have the "same" node in graph multiple times.