2 This question is about a simply connected network with at least three arcs joining 4 nodes. The weights on the arcs are all different and any direct paths always have a smaller weight than the total weight of any indirect paths between two vertices.

1. Kruskal's algorithm is used to construct a minimum connector. Explain why the arcs with the smallest and second smallest weights will always be included in this minimum connector.
2. Draw a diagram to show that the arc with the third smallest weight need not always be included in a minimum connector.