Suppose arc AD with flow
is added to the feasible spanning tree. Adding a nonbasic arc to a spanning
tree always creates a unique undirected cycle. In this case, that cycle
is AD-DE-EC-CA. If the flow
is added to arc AD, then the other arcs in the cycle will need to be adjusted
to retain the required net flow at each node. The effect of adding the
flow
to arc AD on each of the other flows in the cycle is shown in the network
above. |