B$1$ Write a function NearestPoint$($G$,$v$,$mylist$)$ which takes as input a networkx object $G$ representing a weighted graph, an object $v$ which will be a node of $G,$ and a list mylist of some other nodes of G$.$ The function should return whichever node in mylist is nearest to $v($in the sense of the minimum weight path from v$).$ In the event of a tie, it should return the nearest node which appears earliest in mylist.

CORDELIA WEBB UNIVERSITY OF LEEDS, $2023/24$

B$2$ We say that a weighted graph has the Unique Weight Property $($UWP$)$ if no two edges have the same weight. Recall from Workshop $9-10$ that if G is connected and has the UWP then it will automatically have a unique spanning tree. Write a function UWP$($G$)$ which tests whether or not G has the UWP and returns True or False accordingly.

Hint: extract a list of edge$-$weights and use the count function to see how many times each appears.

B$3$ Write a function $GdPath(G,a,b)$ which takes as input a networkx object $G$ representing a connected weighted graph with UWP and objects $a,b$ which will be nodes of G$.$ Your function should return True if the shortest path from a to b lies entirely inside the unique minimal connector and False otherwise.