Apologies if this is a repeat, or just plain silly. I do not have a strong math background and am struggling find good keywords. I am wondering if there is a body of theory or solution to the following scenario.
- I have N fixed points on a 2-dimensional plot representing nodes from a network graph.
- I have new node with unknown coordinates in relation to the plotted nodes.
- What I do have is the as-yet-unplotted node's relationship to every other node, represented as an edge weight.
Given these conditions, is it possible to extrapolate a best location for the new node, where its distance from each node is proportional to the edge weight? My intuition suggest that, depending on how many nodes are already plotted, it would be theoretically possible to engineer a circumstance in which the new node cannot be placed in 2D space in a way that is "true" to all conditions. Yet doing something along these lines seems like it would produce potentially useful representations of data. Thanks for any help you can offer!