[emadehsan]

if the pipes are cut from a Spanning Tree connecting all the hexagons (like the one you witness once you have solved), then yes, for those give pipe pieces, there should be only one solution.

[jjnoakes]

Is this true? I can almost imagine one puzzle that can create two different spanning trees. Maybe I ought to draw it up to verify.

Spanning trees may be required but not sufficient for a unique solution.

[emadehsan]

You are right. It is possible that branches (pipes) cut from one Spanning Tree might be re-arrangeable into a different Spanning Tree.