Note from the moderators: The author references to “connections between nodes” as “noodles”. This is not official or endorsed terminology, in InstaMAT those are simply called “connections”. The note was added to aid the reader of this post.
Let us drag a new node over a noodle to connect two already present nodes. New input/output connections should be reestablished automatically. This would be paired with an easy shorcut to extricate a node from an already existing connection. Again, this operation should reconnect upstream output with a downstream existing input.
Justification
I often happen to create a node somewhere in the graph and then later I discover I want the exact same node inserted into a node chain somewhere else. Or, it happens, that u just didn’t click the right noodle when u were adding a new node and now you want to relocate it. Instead of having to position the node where I want it and then manually reconnecting the inputs/outputs, I would love this to be automated. A time-saving QoL I am so very used to. 
Implementation Details
This is already present in Blender, and, if I am not mistaken, in other node based editors from competition. I understand this might be difficult to implement for complex nodes such as material make, but for a collapsed single input, single output (grayscale?) nodes, all I need is being able to extricate a node from a noodle and drag and drop it in another place. In Blender’s Node Wrangler addon, this works with Alt+Drag a node with the mouse to extricate, and just drag and drop onto a noodle. It only connects equal data types (color to color, grayscale to grayscale, etc.)
Thanks a lot for considering this. 