Graph Algorithms · Challenge problem

A graph has vertices $w,x,y,z,v$ and weighted edges $wx{:}3, wy{:}5, xy{:}2, xz{:}8, yz{:}4, yv{:}7, zv{:}1$. Its minimum spanning tree has weight $10$. What is the smallest possible total weight of a spanning tree that is NOT the minimum one (uses a different set of edges)?