Creating all possible spanning trees.

I have a question about how to create all possible spanning trees of a given graph. The things we know is the connections between switches and the loads between switches. Not every switch is connected to every switch, instead they have particular shape.

I aim to find minimum spanning tree, therefore I am trying to create all spanning trees by brute force and choose which one minimizes the highest load. Matlab min spanning tree command seems to find the min spanning tree if every switch is connected to every switch.

The commands in Matlab and internet research was not sufficient at the moment so that i am asking here. Thanks.