$($a$)$ Given the graph below, find all the possible paths which corresponds to the breadth first search $($BFS$)$ that can be obtained starting from the node $\text{'}6\text{'}.$ Show your detailed workings for finding the breadth first search traversal $65278311049$ and construct the final spanning tree for same.

$($b$)$ Implement the breadth first search algorithm for the above undirected graph on Python. Using your implemented code, generate and write down two paths for transversing the graph by BFS starting at each of the other nodes. $($For each node, write down two different paths.$)$