I know this question is over a year old, but if you Google "Godot C# GetConnectionList" you end up here as one of the top results, so I wanted to share my solution for anyone who comes across.
I don't claim this is the best solution, or even the most correct, but it worked for me.
The following is how I get the fist from and to GraphNodes from the GraphEdit connection list:
var graph = GetNode<GraphEdit>("GraphEdit");
Array connectionList = graph.GetConnectionList;
var from = graph.GetNode<GraphNode>(
var to = graph.GetNode<GraphNode>(