The all$\_$paths function takes in three parameters: start$\_$node, target$\_$value, and path $($with an optional default value of an empty list$).$ It uses a recursive approach to find all the paths from the start$\_$node to the node with the target$\_$value.$$

It appends the current node to the path and checks if it has reached the target value. If so$,$ it returns the current path as a list of nodes.

$$If not, it continues the search through the neighbors and appends all the resulting paths to the paths list.$$

Finally, it returns the paths list, which contains all the paths from the start$\_$node to the target node.