if all the nodes have been visitedwe pop the top of the stack if the stack graph_stack is not emptywe assign the node on top of the stack to node and start the beginning of another execution of the body of the while loop the statement set(adj_nodesissubset(set(visited_vertices)will evaluate to true if all the nodes in adj_nodes are subset of visited_vertices if the if statement failsit means that some nodes remain to be visited we obtain that list of nodes with remaining_elements set(adj_nodesdifference(set(visited_vertices)from the diagramnodes and will be stored in remaining_elements we will access the list in alphabetical orderfirst_adj_node sorted(remaining_elements)[ graph_stack append(first_adj_nodenode first_adj_node we sort remaining_elements and return the first node to first_adj_node this will return we push node onto the stack by appending it to the graph_stack we prepare node for access by assigning it to node on the next iteration of the while loopwe add node to the list of visited nodes we discover that the only adjacent node to bwhich is ahas already been visited because all the adjacent nodes of have been visitedwe pop it off the stackleaving node as the only element on the stack we return to node and examine whether all of its adjacent nodes have been visited the node now has as the only unvisited node we push to the stack and begin the whole process again the output of the traversal is - - - - - - - - depth-first searches find application in solving maze problemsfinding connected componentsand finding the bridges of graphamong others other useful graph methods very oftenyou are concerned with finding path between two nodes you may also want to find all the paths between nodes another useful method would be to find the shortest path between nodes in an unweighted graphthis would simply be the path with the lowest number of edges between them in weighted graphas you have seenthis could involve calculating the total weight of passing through set of edges of coursein different situationyou may want to find the longest or shortest path