Write Python code for the below problem statement using Hill Climbing Algorithm.

Problem statement Given below are the shared and distributed servers placed at various locations in your city. Now imagine it to be in a crisis and you have been asked to compromise some communication lines and keep a minimum number of connections to keep the network up and going. You are required to find the sub set of connections for your work to go un-interrupted. The edge costs depicted below is an approximation towards the transmission cost between any pair of nodes. For heuristic design, consider all the possible paths between any arbitrary node n to the goal node. Dynamically get the start and goal city while execution as inputs. The average of the total transmission cost across all these paths is the heuristic value h(n)