Find minimum weight for disconnection between two nodes in a undirected graph

Question

I want to get minimum weight for disconnection between two particular nodes in a undirected graph. Each nodes and edges in the graph have their own weight.

Those two nodes could be disconnected by deleting some weight in many different ways. So, I want to get minimum value of deleted weight for disconnection.

In the below example, I want to get minimum weight for disconnection between Lidcombe and Redfern and the result is 2. Example of graph

I tried to build an algorithm but failed so I beg your help. Thank you.

Answer 1

https://web.williams.edu/Mathematics/sjmiller/public_html/hudson/Eusden_maxflowmincut.pdf starts with a nice historical version of this problem. During the cold war, working out the most efficient way to disconnect East Germany from the Soviet Union if war broke out. The answer suggested here is to use max-flow/min-cut by running the Ford-Fulkerson algorithm. The disconnection you want is specified by the min cut.